{"id":4839,"date":"2026-09-23T19:59:54","date_gmt":"2026-09-23T10:59:54","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4839"},"modified":"2026-09-23T19:59:55","modified_gmt":"2026-09-23T10:59:55","slug":"how-to-assess-stationarity-of-time-series-in-r-combining-the-adf-and-kpss-tests","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-assess-stationarity-of-time-series-in-r-combining-the-adf-and-kpss-tests\/","title":{"rendered":"\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u306e\u5b9a\u5e38\u6027\u3092R\u3067\u5224\u5b9a\u3059\u308b\u65b9\u6cd5\uff5cADF\u691c\u5b9a\u3068KPSS\u691c\u5b9a\u306e\u7d44\u307f\u5408\u308f\u305b\u65b9"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u5f8c\u8f29<\/strong>\uff1a\u300c\u5148\u8f29\u3001\u3053\u306e\u524d\u6559\u308f\u3063\u305f<a href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-test-whether-a-time-series-is-increasing-in-r-mann-kendall-test-and-sens-slope\/\">Mann-Kendall\u691c\u5b9a<\/a>\u3092\u3001\u3042\u308b\u5730\u70b9\u306e\u5e74\u5e73\u5747\u6c17\u6e29100\u5e74\u5206\u306b\u4f7f\u3063\u3066\u307f\u305f\u3093\u3067\u3059\u3002P &lt; 0.05\u3067\u3001\u3057\u3063\u304b\u308a\u300e\u5897\u3048\u3066\u3044\u308b\u300f\u3068\u51fa\u307e\u3057\u305f\uff01\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5148\u8f29<\/strong>\uff1a\u300c\u30b0\u30e9\u30d5\u306f\u898b\u305f\u304b\u3044\uff1f\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5f8c\u8f29<\/strong>\uff1a\u300c\u306f\u3044\u3001\u53f3\u80a9\u4e0a\u304c\u308a\u3067\u3059\u3002\u6e29\u6696\u5316\u306e\u5f71\u97ff\u3067\u3059\u3088\u306d\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5148\u8f29<\/strong>\uff1a\u300c\u305d\u3046\u304b\u3082\u3057\u308c\u306a\u3044\u3002\u3067\u3082\u3001\u540c\u3058\u3088\u3046\u306a\u53f3\u80a9\u4e0a\u304c\u308a\u306e\u30b0\u30e9\u30d5\u306f\u3001<strong>\u6bce\u5e74\u306e\u63fa\u308c\u304c\u305f\u3060\u7a4d\u307f\u91cd\u306a\u3063\u305f\u3060\u3051<\/strong>\u306e\u7cfb\u5217\u304b\u3089\u3082\u7c21\u5358\u306b\u51fa\u3066\u304f\u308b\u3093\u3060\u3002\u30b3\u30a4\u30f3\u3092\u6295\u3052\u3066\u8868\u306a\u3089+1\u3001\u88cf\u306a\u3089\u22121\u3092\u8db3\u3057\u7d9a\u3051\u308b\u3068\u3001\u305f\u307e\u305f\u307e\u8868\u306e\u591a\u3044\u6642\u671f\u304c\u7d9a\u3044\u3066\u3001\u3057\u3070\u3089\u304f\u4e0a\u304c\u308a\u7d9a\u3051\u308b\u3053\u3068\u304c\u3042\u308b\u3060\u308d\u3046\uff1f\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5f8c\u8f29<\/strong>\uff1a\u300c\u2026\u2026\u305d\u308c\u3060\u3068\u3001\u300e\u5897\u3048\u3066\u3044\u308b\u300f\u306e\u610f\u5473\u304c\u307e\u3063\u305f\u304f\u9055\u3044\u307e\u3059\u306d\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5148\u8f29<\/strong>\uff1a\u300c\u305d\u3046\u306a\u3093\u3060\u3002\u4e00\u5b9a\u306e\u5742\u3092\u4e0a\u3063\u3066\u3044\u308b\uff08<strong>\u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38<\/strong>\uff09\u306e\u304b\u3001\u884c\u304d\u5148\u306e\u6c7a\u307e\u3063\u3066\u3044\u306a\u3044\u6563\u6b69\u304c\u305f\u307e\u305f\u307e\u4e0a\u306b\u5411\u304b\u3063\u305f\uff08<strong>\u5358\u4f4d\u6839\uff1d\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af<\/strong>\uff09\u306e\u304b\u3067\u3001\u5206\u6790\u306e\u3084\u308a\u65b9\u3082\u7d50\u8ad6\u3082\u5909\u308f\u308b\u3002\u3053\u308c\u3092\u898b\u5206\u3051\u308b\u306e\u304c <strong>ADF\u691c\u5b9a<\/strong> \u3068 <strong>KPSS\u691c\u5b9a<\/strong> \u3060\u3002\u305f\u3060\u3057\u7247\u65b9\u3060\u3051\u3067\u306f\u5371\u306a\u3044\u3002<strong>2\u672c\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u4f7f\u3046<\/strong>\u306e\u304c\u30b3\u30c4\u306a\u3093\u3060\u3088\u300d<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u3092\u6271\u3046\u5206\u6790\u306e\u591a\u304f\u306f\u3001\u7cfb\u5217\u304c <strong>\u5b9a\u5e38\uff08stationary\uff09<\/strong> \u3067\u3042\u308b\u3053\u3068\u3092\u524d\u63d0\u306b\u3057\u3066\u3044\u308b\u3002ARIMA\u30e2\u30c7\u30eb\u3082\u305d\u3046\u3060\u3057\u30012\u3064\u306e\u7cfb\u5217\u306e\u95a2\u9023\u3092\u56de\u5e30\u3067\u8abf\u3079\u308b\u5834\u5408\u3082\u540c\u3058\u3067\u3042\u308b\u3002\u975e\u5b9a\u5e38\u306a\u7cfb\u5217\u3069\u3046\u3057\u3092\u56de\u5e30\u3059\u308b\u3068\u3001\u307e\u3063\u305f\u304f\u7121\u95a2\u4fc2\u306a\u7cfb\u5217\u3067\u3082R\u00b2\u304c\u9ad8\u304f\u300c\u6709\u610f\u306a\u95a2\u9023\u300d\u304c\u51fa\u3066\u3057\u307e\u3046\u3002\u3053\u308c\u304c <strong>\u898b\u305b\u304b\u3051\u306e\u56de\u5e30\uff08spurious regression\uff09<\/strong> \u3067\u3042\u308b\uff08Granger &amp; Newbold, 1974\uff09\u3002\u4f8b\u3048\u3070\u30012\u3064\u306e\u7269\u4fa1\u6307\u6570\u3092\u56de\u5e30\u3057\u305f\u3089R\u00b2\u304c0.9\u3060\u3063\u305f\u3001\u3068\u3044\u3046\u7d50\u679c\u306f\u3001\u3053\u306e\u7f60\u306e\u5178\u578b\u4f8b\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u554f\u984c\u306f\u7d4c\u6e08\u30fb\u91d1\u878d\u3067\u6700\u521d\u306b\u6ce8\u76ee\u3055\u308c\u305f\u304c\u3001\u6c17\u6e29\u3084\u6cb3\u5ddd\u6d41\u91cf\u306a\u3069\u306e\u74b0\u5883\u30c7\u30fc\u30bf\u3001\u611f\u67d3\u75c7\u306e\u5831\u544a\u6570\u3084\u5165\u9662\u4ef6\u6570\u306a\u3069\u306e\u516c\u8846\u885b\u751f\u30c7\u30fc\u30bf\u3067\u3082\u3001\u307e\u3063\u305f\u304f\u540c\u3058\u3053\u3068\u304c\u8d77\u3053\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u8a18\u4e8b\u3067\u306f\u3001\u6b21\u306e3\u70b9\u3092R\u3067\u78ba\u8a8d\u3059\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u300c\u5b9a\u5e38\u300d\u300c\u975e\u5b9a\u5e38\u300d\u300c\u5358\u4f4d\u6839\u300d\u3068\u306f\u4f55\u304b\u3092\u3001\u6bd4\u55a9\u3067\u76f4\u611f\u7684\u306b\u7406\u89e3\u3059\u308b<\/li>\n\n\n\n<li>ADF\u691c\u5b9a\u3068KPSS\u691c\u5b9a\u306f <strong>\u5e30\u7121\u4eee\u8aac\u304c\u9006<\/strong> \u3067\u3042\u308a\u30012\u3064\u3092\u7d44\u307f\u5408\u308f\u305b\u305f <strong>4\u901a\u308a\u306e\u5224\u5b9a\u8868<\/strong> \u3067\u8aad\u3080<\/li>\n\n\n\n<li>\u30c8\u30ec\u30f3\u30c9\u306e\u578b\u306e\u6307\u5b9a\u30df\u30b9\u3084\u69cb\u9020\u5909\u5316\uff08\u4ecb\u5165\uff09\u3068\u3044\u3063\u305f\u3001\u5224\u5b9a\u3092\u8aa4\u3089\u305b\u308b\u7f60\u3068\u305d\u306e\u5bfe\u51e6<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u6642\u7cfb\u5217\u5206\u6790\u306e\u57fa\u672c\uff08<code>diff()<\/code>\u30fb<code>acf()<\/code>\u30fb<code>PP.test()<\/code>\u30fb<code>auto.arima()<\/code>\uff09\u306f\u4ee5\u524d\u306e\u8a18\u4e8b\u3067\u89e3\u8aac\u3057\u3066\u3044\u308b\u3002\u524d\u56de\u306f <code>PP.test()<\/code> \u3067\u5b9a\u5e38\u6027\u3092\u3056\u3063\u3068\u78ba\u304b\u3081\u305f\u304c\u3001\u4eca\u56de\u306f\u305d\u306e\u90e8\u5206\u3092\u6398\u308a\u4e0b\u3052\u308b\u7d9a\u7de8\u306b\u3042\u305f\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#x1f449; <a href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/basics-of-time-series-analysis\/\">R\u3067\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u5206\u6790\u3092\u884c\u3046\u65b9\u6cd5<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">1. \u5b9a\u5e38\u3068\u975e\u5b9a\u5e38\uff1a\u300c\u30ea\u30fc\u30c9\u306b\u3064\u306a\u304c\u308c\u305f\u72ac\u300d\u3068\u300c\u30ea\u30fc\u30c9\u306e\u5916\u308c\u305f\u72ac\u300d<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b9a\u5e38\u306a\u7cfb\u5217\u306f\u3001\u5e73\u5747\u306e\u307e\u308f\u308a\u306b\u623b\u3063\u3066\u304f\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u516c\u5712\u3067\u3001\u98fc\u3044\u4e3b\u304c1\u304b\u6240\u306b\u7acb\u3063\u3066\u72ac\u3092\u6563\u6b69\u3055\u305b\u3066\u3044\u308b\u5834\u9762\u3092\u601d\u3044\u6d6e\u304b\u3079\u3066\u307b\u3057\u3044\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u30ea\u30fc\u30c9\u306b\u3064\u306a\u304c\u308c\u305f\u72ac<\/strong>\uff1a\u3042\u3061\u3053\u3061\u52d5\u304d\u56de\u308b\u304c\u3001\u98fc\u3044\u4e3b\uff08\u5e73\u5747\uff09\u304b\u3089\u4e00\u5b9a\u4ee5\u4e0a\u306f\u96e2\u308c\u3089\u308c\u305a\u3001\u3044\u305a\u308c\u623b\u3063\u3066\u304f\u308b\u3002\u4f55\u6642\u306b\u5199\u771f\u3092\u64ae\u3063\u3066\u3082\u3001\u300c\u98fc\u3044\u4e3b\u306e\u307e\u308f\u308a\u3001\u534a\u5f84\u6570\u30e1\u30fc\u30c8\u30eb\u300d\u3068\u3044\u3046\u540c\u3058\u3088\u3046\u306a\u4f4d\u7f6e\u306b\u5199\u308b\u3002\u3053\u308c\u304c <strong>\u5b9a\u5e38\u306a\u7cfb\u5217<\/strong> \u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u30ea\u30fc\u30c9\u306e\u5916\u308c\u305f\u72ac<\/strong>\uff1a\u4e00\u6b69\u4e00\u6b69\u306f\u3067\u305f\u3089\u3081\u3060\u304c\u3001\u623b\u3063\u3066\u304f\u308b\u529b\u304c\u50cd\u304b\u306a\u3044\u306e\u3067\u3001\u6642\u9593\u304c\u305f\u3064\u307b\u3069\u98fc\u3044\u4e3b\u304b\u3089\u9060\u304f\u3078\u884c\u3063\u3066\u3057\u307e\u3046\u53ef\u80fd\u6027\u304c\u9ad8\u304f\u306a\u308b\u300210\u5206\u5f8c\u30681\u6642\u9593\u5f8c\u3067\u306f\u3001\u3044\u305d\u3046\u306a\u7bc4\u56f2\u306e\u5e83\u3055\u304c\u307e\u308b\u3067\u9055\u3046\u3002\u3053\u308c\u304c <strong>\u975e\u5b9a\u5e38\u306a\u7cfb\u5217<\/strong>\uff08\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\uff09\u3067\u3042\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1a\u5b9a\u5e38\u3068\u306f<\/strong><br>\u6642\u7cfb\u5217\u5206\u6790\u3067\u300c\u5b9a\u5e38\u300d\u3068\u8a00\u3046\u3068\u304d\u3001\u591a\u304f\u306f <strong>\u5f31\u5b9a\u5e38\uff08weak stationarity\uff09<\/strong> \u3092\u6307\u3059\u3002\u6b21\u306e3\u6761\u4ef6\u304c\u305d\u308d\u3063\u305f\u72b6\u614b\u3067\u3042\u308b\u3002<br>\u2460 \u5e73\u5747\u304c\u6642\u70b9\u306b\u3088\u3089\u305a\u4e00\u5b9a\u3067\u3042\u308b<br>\u2461 \u5206\u6563\u304c\u6642\u70b9\u306b\u3088\u3089\u305a\u4e00\u5b9a\u3067\u3042\u308b<br>\u2462 2\u6642\u70b9\u9593\u306e\u5171\u5206\u6563\uff08\u81ea\u5df1\u5171\u5206\u6563\uff09\u304c\u3001\u6642\u70b9\u305d\u306e\u3082\u306e\u3067\u306f\u306a\u304f <strong>\u6642\u70b9\u306e\u5dee\uff08\u30e9\u30b0\uff09\u3060\u3051<\/strong> \u3067\u6c7a\u307e\u308b<br>\u2462\u306f\u300c1\u6708\u30682\u6708\u306e\u95a2\u4fc2\u300d\u3068\u300c7\u6708\u30688\u6708\u306e\u95a2\u4fc2\u300d\u304c\u540c\u3058\u5f37\u3055\u3067\u3042\u308b\u3001\u3068\u3044\u3046\u610f\u5473\u3060\u3002\u5b63\u7bc0\u5909\u52d5\u306e\u306a\u3044\u5b89\u5b9a\u3057\u305f\u7cfb\u5217\u3001\u4f8b\u3048\u3070\u8a2d\u5099\u304c\u4e00\u5b9a\u306e\u5de5\u5834\u306e\u65e5\u3005\u306e\u4e0d\u826f\u54c1\u7387\u306a\u3069\u304c\u3001\u5b9a\u5e38\u306b\u8fd1\u3044\u4f8b\u3067\u3042\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1a\u975e\u5b9a\u5e38\u3068\u306f<\/strong><br>\u4e0a\u306e3\u6761\u4ef6\u306e\u3069\u308c\u304b\u304c\u5d29\u308c\u305f\u7cfb\u5217\u3092 <strong>\u975e\u5b9a\u5e38<\/strong> \u3068\u547c\u3076\u3002\u5178\u578b\u7684\u306a\u5d29\u308c\u65b9\u306f2\u7a2e\u985e\u3042\u308b\u3002<br>\u30fb<strong>\u78ba\u7387\u30c8\u30ec\u30f3\u30c9\uff08\u5358\u4f4d\u6839\uff09<\/strong>\uff1a\u30e9\u30f3\u30c0\u30e0\u306a\u30b7\u30e7\u30c3\u30af\u304c\u6d88\u3048\u305a\u306b\u7a4d\u307f\u91cd\u306a\u308a\u3001\u7cfb\u5217\u304c\u6f02\u6d41\u3057\u3066\u3044\u304f\u3002\u682a\u4fa1\u3084\u70ba\u66ff\u30ec\u30fc\u30c8\u304c\u4ee3\u8868\u4f8b\u3067\u3042\u308b\u3002<br>\u30fb<strong>\u78ba\u5b9a\u30c8\u30ec\u30f3\u30c9<\/strong>\uff1a\u4e00\u5b9a\u306e\u5742\uff08\u76f4\u7dda\u306a\u3069\uff09\u306e\u4e0a\u3067\u3001\u63fa\u3089\u304e\u81ea\u4f53\u306f\u5b9a\u5e38\u3067\u3042\u308b\u3002\u5742\u3092\u53d6\u308a\u9664\u3051\u3070\u5b9a\u5e38\u306b\u623b\u308b\u3002\u4f8b\u3048\u3070\u3001\u6c17\u5019\u5909\u52d5\u306b\u3088\u308b\u6c17\u6e29\u306e\u4e0a\u6607\u306f\u3001\u3053\u306e\u30bf\u30a4\u30d7\u3068\u3057\u3066\u30e2\u30c7\u30eb\u5316\u3055\u308c\u308b\u3053\u3068\u304c\u3042\u308b\u3002<br>\u3069\u3061\u3089\u3082\u898b\u305f\u76ee\u306f\u300c\u53f3\u80a9\u4e0a\u304c\u308a\u300d\u306b\u306a\u308a\u3046\u308b\u306e\u3067\u3001\u30b0\u30e9\u30d5\u3060\u3051\u3067\u306f\u533a\u5225\u3057\u306b\u304f\u3044\u3002<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">\u5358\u4f4d\u6839\uff1a\u30b7\u30e7\u30c3\u30af\u306e\u300c\u8a18\u61b6\u300d\u304c\u6d88\u3048\u308b\u304b\u3069\u3046\u304b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6570\u5f0f\u306f\u6700\u5c0f\u9650\u306b\u3057\u3066\u30011\u672c\u3060\u3051\u793a\u3059\u3002\u4eca\u5e74\u306e\u5024 $y_t$ \u304c\u3001\u6628\u5e74\u306e\u5024 $y_{t-1}$ \u3068\u4eca\u5e74\u306e\u30e9\u30f3\u30c0\u30e0\u306a\u30b7\u30e7\u30c3\u30af $\\varepsilon_t$ \u3067\u6c7a\u307e\u308b\u30e2\u30c7\u30eb\uff081\u6b21\u306e\u81ea\u5df1\u56de\u5e30\u3001AR(1)\uff09\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>y_t = \\rho , y_{t-1} + \\varepsilon_t<br>$$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$|\\rho| &lt; 1$ \u306e\u3068\u304d\uff1a\u30b7\u30e7\u30c3\u30af\u306e\u5f71\u97ff\u306f\u6bce\u5e74 $\\rho$ \u500d\u305a\u3064\u5c0f\u3055\u304f\u306a\u308a\u3001\u3084\u304c\u3066\u6d88\u3048\u308b \u2192 <strong>\u5b9a\u5e38<\/strong><\/li>\n\n\n\n<li>$\\rho = 1$ \u306e\u3068\u304d\uff1a\u30b7\u30e7\u30c3\u30af\u306e\u5f71\u97ff\u304c100%\u7fcc\u5e74\u306b\u6301\u3061\u8d8a\u3055\u308c\u3001\u6c38\u9060\u306b\u6d88\u3048\u306a\u3044 \u2192 <strong>\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\uff08\u5358\u4f4d\u6839\uff09<\/strong><\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1a\u5358\u4f4d\u6839\u3068\u306f<\/strong><br>\u6c60\u306b\u77f3\u3092\u6295\u3052\u308b\u5834\u9762\u3092\u60f3\u50cf\u3057\u3066\u307b\u3057\u3044\u3002\u666e\u901a\u306e\u6c60\uff08$\\rho &lt; 1$\uff09\u306a\u3089\u3001\u6ce2\u7d0b\u306f\u5e83\u304c\u308a\u306a\u304c\u3089\u5f31\u307e\u308a\u3001\u3084\u304c\u3066\u6c34\u9762\u306f\u5143\u306e\u9759\u3051\u3055\u306b\u623b\u308b\u3002\u3068\u3053\u308d\u304c\u5358\u4f4d\u6839\u306e\u3042\u308b\u6c60\uff08$\\rho = 1$\uff09\u3067\u306f\u3001\u77f3\u3092\u6295\u3052\u308b\u305f\u3073\u306b <strong>\u6c34\u4f4d\u305d\u306e\u3082\u306e\u304c\u4e0a\u304c\u3063\u305f\u307e\u307e\uff08\u3042\u308b\u3044\u306f\u4e0b\u304c\u3063\u305f\u307e\u307e\uff09<\/strong> \u306b\u306a\u308b\u3002\u904e\u53bb\u306b\u6295\u3052\u305f\u3059\u3079\u3066\u306e\u77f3\u306e\u5f71\u97ff\u304c\u3001\u8db3\u3057\u7b97\u3067\u4eca\u306e\u6c34\u4f4d\u306b\u6b8b\u308a\u7d9a\u3051\u308b\u306e\u3067\u3042\u308b\u3002<br>\u300c\u5358\u4f4d\u6839\u300d\u3068\u3044\u3046\u540d\u524d\u306f\u3001\u3053\u306e\u30e2\u30c7\u30eb\u306e\u7279\u6027\u65b9\u7a0b\u5f0f $1 &#8211; \\rho z = 0$ \u306e\u6839 $z = 1\/\\rho$ \u304c\u3001$\\rho = 1$ \u306e\u3068\u304d\u306b\u3061\u3087\u3046\u3069 <strong>1\uff08\u5358\u4f4d\uff09<\/strong> \u306b\u306a\u308b\u3053\u3068\u306b\u7531\u6765\u3059\u308b\u3002\u540d\u524d\u306f\u6570\u5b66\u7684\u3060\u304c\u3001\u610f\u5473\u306f\u300c\u30b7\u30e7\u30c3\u30af\u306e\u8a18\u61b6\u304c\u6d88\u3048\u306a\u3044\u300d\u3068\u899a\u3048\u3066\u304a\u3051\u3070\u3088\u3044\u3002<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">\u300c\u5dee\u5206\u3092\u53d6\u308b\u300d\u304b\u300c\u30c8\u30ec\u30f3\u30c9\u3092\u9664\u304f\u300d\u304b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2\u7a2e\u985e\u306e\u975e\u5b9a\u5e38\u306f\u3001\u5bfe\u51e6\u6cd5\u304c\u7570\u306a\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u7cfb\u5217\u306e\u30bf\u30a4\u30d7<\/th><th>\u4e2d\u8eab<\/th><th>\u5b9a\u5e38\u306b\u3059\u308b\u65b9\u6cd5<\/th><\/tr><\/thead><tbody><tr><td>\u5dee\u5206\u5b9a\u5e38\uff08\u5358\u4f4d\u6839\uff09<\/td><td>\u30b7\u30e7\u30c3\u30af\u304c\u7a4d\u307f\u91cd\u306a\u3063\u3066\u6f02\u6d41\u3059\u308b<\/td><td><strong>\u5dee\u5206<\/strong>\uff08$y_t &#8211; y_{t-1}$\uff09\u3092\u53d6\u308b<\/td><\/tr><tr><td>\u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38<\/td><td>\u76f4\u7dda\u306e\u5742\uff0b\u5b9a\u5e38\u306a\u63fa\u3089\u304e<\/td><td><strong>\u30c8\u30ec\u30f3\u30c9\u3092\u9664\u304f<\/strong>\uff08\u56de\u5e30\u306e\u6b8b\u5dee\u3092\u4f7f\u3046\u3001\u306a\u3069\uff09<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bfe\u51e6\u3092\u53d6\u308a\u9055\u3048\u308b\u3068\u3001\u5206\u6790\u304c\u3086\u304c\u3080\u3002\u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38\u306e\u7cfb\u5217\u306b\u5dee\u5206\u3092\u53d6\u308b\u3068\u3001\u4f59\u5206\u306a\u8ca0\u306e\u81ea\u5df1\u76f8\u95a2\u304c\u751f\u307e\u308c\u308b\uff08\u904e\u5270\u5dee\u5206\uff09\u3002\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u304b\u3089\u76f4\u7dda\u3092\u5f15\u304d\u7b97\u3057\u3066\u3082\u3001\u6f02\u6d41\u306f\u6b8b\u3063\u305f\u307e\u307e\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5192\u982d\u306e\u6c17\u6e29\u306e\u8a71\u306b\u623b\u308d\u3046\u3002\u7cfb\u5217\u304c\u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38\u306a\u3089\u3001\u300c\u5e74\u3042\u305f\u308a\u4f55\u5ea6\u4e0a\u304c\u3063\u3066\u3044\u308b\u304b\u300d\u3092\u8a9e\u308b\u306e\u306b <a href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-test-whether-a-time-series-is-increasing-in-r-mann-kendall-test-and-sens-slope\/\">Mann-Kendall\u691c\u5b9a\u3068Sen&#8217;s slope<\/a> \u304c\u5f79\u306b\u7acb\u3064\u3002\u4e00\u65b9\u3001\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u3067\u306f\u5f37\u3044\u81ea\u5df1\u76f8\u95a2\u306e\u305b\u3044\u3067\u3001MK\u691c\u5b9a\u304c\u300c\u6709\u610f\u306a\u30c8\u30ec\u30f3\u30c9\u300d\u3092\u51fa\u3057\u3084\u3059\u304f\u306a\u308b\uff08MK\u8a18\u4e8b\u306e\u300c\u7f60\u2460\uff1a\u81ea\u5df1\u76f8\u95a2\u300d\u3068\u540c\u3058\u69cb\u56f3\u3067\u3042\u308b\uff09\u3002\u3060\u304b\u3089\u3053\u305d\u3001\u30c8\u30ec\u30f3\u30c9\u3092\u8a9e\u308b\u524d\u306b\u3001\u7cfb\u5217\u306e\u30bf\u30a4\u30d7\u3092\u78ba\u304b\u3081\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2. \u6b63\u653b\u6cd5\uff1a\u5e30\u7121\u4eee\u8aac\u304c\u9006\u306e2\u3064\u306e\u691c\u5b9a\u3092\u7d44\u307f\u5408\u308f\u305b\u308b<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">ADF\u691c\u5b9a\uff1a\u5e30\u7121\u4eee\u8aac\u306f\u300c\u5358\u4f4d\u6839\u3042\u308a\u300d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>ADF\u691c\u5b9a\uff08Augmented Dickey-Fuller test\uff09<\/strong> \u306f\u3001Dickey &amp; Fuller\uff081979\uff09\u306e\u691c\u5b9a\u3092\u3001Said &amp; Dickey\uff081984\uff09\u304c\u81ea\u5df1\u76f8\u95a2\u306e\u5f37\u3044\u4e00\u822c\u7684\u306a\u7cfb\u5217\u306b\u3082\u4f7f\u3048\u308b\u3088\u3046\u62e1\u5f35\u3057\u305f\u3082\u306e\u3067\u3042\u308b\u3002\u4e0a\u306eAR(1)\u306e\u5f0f\u3092\u5909\u5f62\u3057\u305f\u6b21\u306e\u56de\u5e30\u3067\u3001$\\gamma = \\rho &#8211; 1$ \u304c0\u304b\u3069\u3046\u304b\u3092\u8abf\u3079\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\Delta y_t = \\alpha + \\beta t + \\gamma , y_{t-1} + \\sum_{i=1}^{k} \\delta_i , \\Delta y_{t-i} + \\varepsilon_t<br>$$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5e30\u7121\u4eee\u8aac H0<\/strong>\uff1a$\\gamma = 0$\uff08\u5358\u4f4d\u6839\u3042\u308a\uff1d\u975e\u5b9a\u5e38\uff09<\/li>\n\n\n\n<li><strong>\u5bfe\u7acb\u4eee\u8aac H1<\/strong>\uff1a$\\gamma &lt; 0$\uff08\u5b9a\u5e38\uff09<\/li>\n\n\n\n<li>\u6700\u5f8c\u306e\u548c\u306e\u9805\uff08$\\Delta y$ \u306e\u30e9\u30b0 $k$ \u500b\uff09\u304c &#8220;Augmented&#8221; \u306e\u90e8\u5206\u3067\u3001\u6b8b\u5dee\u306e\u81ea\u5df1\u76f8\u95a2\u3092\u5438\u53ce\u3059\u308b\u5f79\u5272\u304c\u3042\u308b<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u56de\u5e30\u5f0f\u306b\u4f55\u3092\u5165\u308c\u308b\u304b\u3067\u3001<strong>3\u3064\u306e\u578b<\/strong> \u304c\u3042\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u578b\uff08<code>urca::ur.df<\/code> \u306e <code>type<\/code>\uff09<\/th><th>\u56de\u5e30\u5f0f\u306e\u4e2d\u8eab<\/th><th>\u60f3\u5b9a\u3059\u308b\u7cfb\u5217<\/th><\/tr><\/thead><tbody><tr><td><code>\"none\"<\/code><\/td><td>\u5b9a\u6570\u9805\u306a\u3057\u30fb\u30c8\u30ec\u30f3\u30c9\u306a\u3057<\/td><td>\u5e73\u57470\u306e\u307e\u308f\u308a\u3092\u52d5\u304f\u7cfb\u5217<\/td><\/tr><tr><td><code>\"drift\"<\/code><\/td><td>\u5b9a\u6570\u9805\u306e\u307f<\/td><td>0\u3067\u306a\u3044\u4e00\u5b9a\u306e\u5e73\u5747\u306e\u307e\u308f\u308a\u3092\u52d5\u304f\u7cfb\u5217<\/td><\/tr><tr><td><code>\"trend\"<\/code><\/td><td>\u5b9a\u6570\u9805\uff0b\u30c8\u30ec\u30f3\u30c9\u9805<\/td><td>\u53f3\u80a9\u4e0a\u304c\u308a\u30fb\u53f3\u80a9\u4e0b\u304c\u308a\u306e\u7cfb\u5217<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u30e9\u30b0\u6b21\u6570 $k$ \u306e\u9078\u3073\u65b9<\/strong> \u306b\u3082\u6ce8\u610f\u304c\u3044\u308b\u3002\u5c11\u306a\u3059\u304e\u308b\u3068\u6b8b\u5dee\u306b\u81ea\u5df1\u76f8\u95a2\u304c\u6b8b\u308a\u3001\u7b2c1\u7a2e\u306e\u904e\u8aa4\uff08\u672c\u5f53\u306f\u5358\u4f4d\u6839\u304c\u3042\u308b\u306e\u306b\u300c\u5b9a\u5e38\u300d\u3068\u5224\u5b9a\u3059\u308b\u8aa4\u308a\uff09\u304c\u5897\u3048\u308b\u3002\u591a\u3059\u304e\u308b\u3068\u691c\u51fa\u529b\u304c\u843d\u3061\u308b\u3002AIC\u3084BIC\u3067\u9078\u3076\u306e\u304c\u4e00\u822c\u7684\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">KPSS\u691c\u5b9a\uff1a\u5e30\u7121\u4eee\u8aac\u306f\u300c\u5b9a\u5e38\u300d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>KPSS\u691c\u5b9a<\/strong>\uff08Kwiatkowski, Phillips, Schmidt &amp; Shin, 1992\uff09\u306f\u3001\u767a\u60f3\u304c\u9006\u3067\u3042\u308b\u3002\u7cfb\u5217\u3092\u6b21\u306e3\u3064\u306e\u90e8\u54c1\u306e\u548c\u3068\u8003\u3048\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>y_t = \\xi t + r_t + \\varepsilon_t, \\qquad r_t = r_{t-1} + u_t<br>$$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$\\xi t$\uff1a\u78ba\u5b9a\u30c8\u30ec\u30f3\u30c9<\/li>\n\n\n\n<li>$r_t$\uff1a\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\uff08\u3070\u3089\u3064\u304d $\\sigma_u^2$\uff09<\/li>\n\n\n\n<li>$\\varepsilon_t$\uff1a\u5b9a\u5e38\u306a\u63fa\u3089\u304e<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u90e8\u54c1\u306e\u3070\u3089\u3064\u304d\u304c0\uff08$\\sigma_u^2 = 0$\uff09\u306a\u3089\u3001$r_t$ \u306f\u52d5\u304b\u306a\u3044\u5b9a\u6570\u306b\u306a\u308a\u3001\u7cfb\u5217\u306f\u5b9a\u5e38\u3067\u3042\u308b\u3002\u305d\u3053\u3067\u3001<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5e30\u7121\u4eee\u8aac H0<\/strong>\uff1a$\\sigma_u^2 = 0$\uff08\u5b9a\u5e38\uff09<\/li>\n\n\n\n<li><strong>\u5bfe\u7acb\u4eee\u8aac H1<\/strong>\uff1a$\\sigma_u^2 &gt; 0$\uff08\u5358\u4f4d\u6839\u3042\u308a\uff09<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3092\u691c\u5b9a\u3059\u308b\u3002\u5e30\u7121\u4eee\u8aac\u306e\u578b\u306f2\u3064\u3042\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u578b\uff08<code>tseries::kpss.test<\/code> \u306e <code>null<\/code> \/ <code>urca::ur.kpss<\/code> \u306e <code>type<\/code>\uff09<\/th><th>\u5e30\u7121\u4eee\u8aac<\/th><\/tr><\/thead><tbody><tr><td><code>\"Level\"<\/code> \/ <code>\"mu\"<\/code><\/td><td>\u4e00\u5b9a\u306e\u6c34\u6e96\u306e\u307e\u308f\u308a\u3067\u5b9a\u5e38\uff08\u6c34\u6e96\u5b9a\u5e38\uff09<\/td><\/tr><tr><td><code>\"Trend\"<\/code> \/ <code>\"tau\"<\/code><\/td><td>\u76f4\u7dda\u30c8\u30ec\u30f3\u30c9\u306e\u307e\u308f\u308a\u3067\u5b9a\u5e38\uff08\u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38\uff09<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">KPSS\u691c\u5b9a\u3067\u306f\u3001\u9577\u671f\u5206\u6563\u3092\u63a8\u5b9a\u3059\u308b\u3068\u304d\u306e <strong>\u5e2f\u57df\u5e45\uff08\u30e9\u30b0\u6570\uff09<\/strong> \u304c\u7d50\u679c\u306b\u5f71\u97ff\u3059\u308b\u3002\u5927\u304d\u3059\u304e\u308b\u3068\u691c\u51fa\u529b\u304c\u843d\u3061\u3001\u5c0f\u3055\u3059\u304e\u308b\u3068\u7b2c1\u7a2e\u306e\u904e\u8aa4\u304c\u5897\u3048\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2\u3064\u306e\u691c\u5b9a\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u5224\u5b9a\u8868<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u304c\u3053\u306e\u8a18\u4e8b\u306e\u4e2d\u5fc3\u3067\u3042\u308b\u30022\u3064\u306e\u691c\u5b9a\u3092\u3001<strong>2\u4eba\u306e\u88c1\u5224\u5b98<\/strong> \u306b\u55a9\u3048\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>ADF\u88c1\u5224\u5b98<\/strong>\u306f\u300c\u88ab\u544a\uff08\u7cfb\u5217\uff09\u306f\u975e\u5b9a\u5e38\u3067\u3042\u308b\u300d\u3068\u3044\u3046\u524d\u63d0\u304b\u3089\u51fa\u767a\u3057\u3001\u5b9a\u5e38\u3067\u3042\u308b\u5341\u5206\u306a\u8a3c\u62e0\u304c\u3042\u308b\u3068\u304d\u3060\u3051\u5224\u6c7a\u3092\u8986\u3059\uff08\uff1d\u300c\u975e\u5b9a\u5e38\u300d\u3092\u63a8\u5b9a\u3059\u308b\u88c1\u5224\u5b98\uff09<\/li>\n\n\n\n<li><strong>KPSS\u88c1\u5224\u5b98<\/strong>\u306f\u300c\u88ab\u544a\u306f\u5b9a\u5e38\u3067\u3042\u308b\u300d\u3068\u3044\u3046\u524d\u63d0\u304b\u3089\u51fa\u767a\u3057\u3001\u975e\u5b9a\u5e38\u3067\u3042\u308b\u5341\u5206\u306a\u8a3c\u62e0\u304c\u3042\u308b\u3068\u304d\u3060\u3051\u5224\u6c7a\u3092\u8986\u3059\uff08\uff1d\u300c\u5b9a\u5e38\u300d\u3092\u63a8\u5b9a\u3059\u308b\u88c1\u5224\u5b98\uff09<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3069\u3061\u3089\u306e\u88c1\u5224\u5b98\u3082\u3001\u8a3c\u62e0\u304c\u8db3\u308a\u306a\u3051\u308c\u3070 <strong>\u524d\u63d0\u3069\u304a\u308a\u306e\u5224\u6c7a\u3092\u51fa\u3059\u3057\u304b\u306a\u3044<\/strong>\u3002ADF\u88c1\u5224\u5b98\u304c\u300c\u975e\u5b9a\u5e38\u300d\u3068\u8a00\u3063\u305f\u306e\u306f\u3001\u5358\u306b\u5b9a\u5e38\u306e\u8a3c\u62e0\u304c\u8db3\u308a\u306a\u304b\u3063\u305f\u3060\u3051\u304b\u3082\u3057\u308c\u306a\u3044\u3002\u3060\u304b\u30892\u4eba\u306e\u610f\u898b\u3092\u7a81\u304d\u5408\u308f\u305b\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>ADF\uff08H0\uff1a\u5358\u4f4d\u6839\uff09<\/th><th>KPSS\uff08H0\uff1a\u5b9a\u5e38\uff09<\/th><th>\u7d50\u8ad6<\/th><\/tr><\/thead><tbody><tr><td>\u68c4\u5374<\/td><td>\u68c4\u5374\u305b\u305a<\/td><td><strong>\u5b9a\u5e38<\/strong>\uff082\u4eba\u306e\u610f\u898b\u304c\u4e00\u81f4\uff09<\/td><\/tr><tr><td>\u68c4\u5374\u305b\u305a<\/td><td>\u68c4\u5374<\/td><td><strong>\u975e\u5b9a\u5e38\uff08\u5358\u4f4d\u6839\uff09<\/strong> \u2192 \u5dee\u5206\u3092\u53d6\u308b\uff082\u4eba\u306e\u610f\u898b\u304c\u4e00\u81f4\uff09<\/td><\/tr><tr><td>\u68c4\u5374<\/td><td>\u68c4\u5374<\/td><td><strong>\u5224\u65ad\u4fdd\u7559<\/strong>\uff1a\u69cb\u9020\u5909\u5316\u3001\u30c8\u30ec\u30f3\u30c9\u306e\u578b\u306e\u6307\u5b9a\u30df\u30b9\u3001\u9577\u671f\u8a18\u61b6\u306a\u3069\u3092\u7591\u3046<\/td><\/tr><tr><td>\u68c4\u5374\u305b\u305a<\/td><td>\u68c4\u5374\u305b\u305a<\/td><td><strong>\u5224\u65ad\u4fdd\u7559<\/strong>\uff1a\u30c7\u30fc\u30bf\u4e0d\u8db3\u30fb\u691c\u51fa\u529b\u4e0d\u8db3\u3002\u3069\u3061\u3089\u3068\u3082\u8a00\u3048\u306a\u3044<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1a\u300c\u68c4\u5374\u3067\u304d\u306a\u3044\u300d\u306f\u300c\u5e30\u7121\u4eee\u8aac\u304c\u6b63\u3057\u3044\u300d\u3067\u306f\u306a\u3044<\/strong><br>ADF\u691c\u5b9a\u3067P = 0.3\u3060\u3063\u305f\u3068\u304d\u3001\u300c\u5358\u4f4d\u6839\u304c\u3042\u308b\uff08\u975e\u5b9a\u5e38\u3060\uff09\u3068\u8a3c\u660e\u3055\u308c\u305f\u300d\u3068\u66f8\u304f\u306e\u306f\u8aa4\u308a\u3067\u3042\u308b\u3002\u8a00\u3048\u308b\u306e\u306f\u300c\u5b9a\u5e38\u3060\u3068\u8a00\u3048\u308b\u5341\u5206\u306a\u8a3c\u62e0\u304c\u306a\u304b\u3063\u305f\u300d\u307e\u3067\u3060\u3002\u7279\u306b\u6570\u5341\u70b9\u7a0b\u5ea6\u306e\u77ed\u3044\u7cfb\u5217\u3067\u306f\u3001ADF\u691c\u5b9a\u306f $\\rho = 0.9$ \u306e\u3088\u3046\u306a\u300c\u5358\u4f4d\u6839\u306b\u8fd1\u3044\u304c\u5b9a\u5e38\u300d\u306a\u7cfb\u5217\u3092\u898b\u5206\u3051\u308b\u529b\u304c\u5f31\u3044\u3002KPSS\u3092\u4f75\u7528\u3059\u308b\u306e\u306f\u3001\u3053\u306e\u5f31\u70b9\u3092\u53cd\u5bfe\u5074\u304b\u3089\u88dc\u3046\u305f\u3081\u3067\u3042\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b9f\u969b\u306e\u7814\u7a76\u3067\u3082\u3001\u3053\u306e\u7d44\u307f\u5408\u308f\u305b\u306f\u4f7f\u308f\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u7d4c\u6e08<\/strong>\uff1aKPSS\u539f\u8457\u306e\u526f\u984c\u306f &#8220;How sure are we that economic time series have a unit root?&#8221; \u3067\u3042\u308b\u3002\u305d\u306e\u80cc\u666f\u306b\u306f\u3001Nelson &amp; Plosser\uff081982\uff09\u304c\u7c73\u56fd\u306e\u9577\u671f\u30de\u30af\u30ed\u7d4c\u6e08\u7cfb\u5217\u306e\u591a\u304f\u3067\u5358\u4f4d\u6839\u3092\u68c4\u5374\u3067\u304d\u306a\u304b\u3063\u305f\u3001\u3068\u3044\u3046\u6709\u540d\u306a\u5831\u544a\u304c\u3042\u308b\u3002KPSS\u306f\u3001\u3053\u306e\u300c\u5358\u4f4d\u6839\u3092\u68c4\u5374\u3067\u304d\u306a\u3044\u300d\u3068\u3044\u3046\u7d50\u679c\u3092\u3001\u5e30\u7121\u4eee\u8aac\u3092\u9006\u306b\u3057\u305f\u691c\u5b9a\u3067\u554f\u3044\u76f4\u3057\u305f\u306e\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u516c\u8846\u885b\u751f<\/strong>\uff1a\u4e2d\u56fd\u30fb\u6cc9\u5dde\u5e02\u306e\u30a4\u30f3\u30d5\u30eb\u30a8\u30f3\u30b6\u4e88\u6e2c\u7814\u7a76\uff08Pan et al., 2025\uff09\u3067\u306f\u3001ADF\u691c\u5b9a\u304cP = 0.047\u3068\u6709\u610f\u6c34\u6e96\u304e\u308a\u304e\u308a\u3060\u3063\u305f\u3002\u305d\u3053\u3067KPSS\u691c\u5b9a\u3092\u8ffd\u52a0\u3057\u305f\u3068\u3053\u308d\u975e\u5b9a\u5e38\u3068\u5224\u5b9a\u3055\u308c\u305f\u305f\u3081\u30011\u56de\u306e\u5dee\u5206\u3092\u53d6\u3063\u3066\u304b\u3089\u30e2\u30c7\u30eb\u5316\u3057\u3066\u3044\u308b\u3002KPSS\u3092\u78ba\u8a8d\u306e\u305f\u3081\u306b\u4f7f\u3063\u305f\u5b9f\u4f8b\u3067\u3042\u308b\u3002\u305f\u3060\u3057\u672c\u6765\u306f\u3001ADF\u306eP\u5024\u304c0.05\u306e\u524d\u5f8c\u304b\u3069\u3046\u304b\u3067\u8ffd\u52a0\u306e\u691c\u5b9a\u3092\u6c7a\u3081\u308b\u306e\u3067\u306f\u306a\u304f\u3001<strong>\u6700\u521d\u304b\u3089\u4e21\u65b9\u3092\u5b9f\u884c\u3057\u3066\u5224\u5b9a\u8868\u3067\u8aad\u3080<\/strong> \u306e\u304c\u671b\u307e\u3057\u3044\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div id=\"biost-2138594227\" class=\"biost- biost-entity-placement\"><p style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><a href=\"https:\/\/best-biostatistics.com\/kmhl\">\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n<a href=\"https:\/\/best-biostatistics.com\/kmhl\"><img class=\"aligncenter wp-image-2794 size-full\" src=\"https:\/\/best-biostatistics.com\/wp\/wp-content\/uploads\/2023\/11\/bn_r_03.png\" alt=\"\" width=\"500\" height=\"327\" \/><\/a>\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000; font-size: 20px;\"><strong><span class=\"marker2\">\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div><h2 class=\"wp-block-heading\">3. R\u3067\u5b9f\u88c5\u3057\u3066\u307f\u3088\u3046\uff08Step by Step\uff09<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u304b\u3089\u306f\u3001\u6027\u8cea\u306e\u308f\u304b\u3063\u3066\u3044\u308b3\u3064\u306e\u7591\u4f3c\u7cfb\u5217\u3092\u4f5c\u308a\u3001ADF\u691c\u5b9a\u3068KPSS\u691c\u5b9a\u304c\u305d\u308c\u305e\u308c\u3092\u3069\u3046\u5224\u5b9a\u3059\u308b\u304b\u3092\u78ba\u304b\u3081\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f7f\u3046\u30d1\u30c3\u30b1\u30fc\u30b8\u306f\u6b21\u306e3\u3064\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>tseries<\/code>\uff1a<code>adf.test()<\/code>\u30fb<code>kpss.test()<\/code> \u3067P\u5024\u307e\u3067\u624b\u65e9\u304f\u51fa\u305b\u308b<\/li>\n\n\n\n<li><code>urca<\/code>\uff1a<code>ur.df()<\/code>\u30fb<code>ur.kpss()<\/code> \u3067\u56de\u5e30\u5f0f\u306e\u578b\u3084\u30e9\u30b0\u3092\u7d30\u304b\u304f\u6307\u5b9a\u3067\u304d\u308b\uff08P\u5024\u3067\u306f\u306a\u304f\u81e8\u754c\u5024\u3067\u5224\u5b9a\u3059\u308b\uff09<\/li>\n\n\n\n<li><code>forecast<\/code>\uff1a<code>ndiffs()<\/code> \u3067\u5fc5\u8981\u306a\u5dee\u5206\u306e\u56de\u6570\u3092\u81ea\u52d5\u3067\u6c7a\u3081\u308b<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u306e\u7d50\u679c\u306f\u3001R 4.6.1\u3001tseries 0.10-63\u3001urca 1.3-4\u3001forecast 9.0.2 \u3067\u5b9f\u969b\u306b\u5b9f\u884c\u3057\u3066\u78ba\u8a8d\u3057\u305f\u3082\u306e\u3067\u3042\u308b\u3002\u4e71\u6570\u3092\u4f7f\u3046\u305f\u3081\u3001<code>set.seed()<\/code> \u306e\u5024\u3084\u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u30d0\u30fc\u30b8\u30e7\u30f3\u304c\u9055\u3046\u3068\u6570\u5024\u306f\u5909\u308f\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 0\uff1a\u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u6e96\u5099<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># install.packages(c(\"tseries\", \"urca\", \"forecast\"))\nlibrary(tseries)\nlibrary(urca)\nlibrary(forecast)<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1\uff1a\u7591\u4f3c\u30c7\u30fc\u30bf\u3092\u4f5c\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c\u3042\u308b\u5730\u70b9\u306e\u5e74\u5e73\u5747\u6c17\u6e29\uff081926\u301c2025\u5e74\u3001100\u5e74\u5206\uff09\u300d\u3092\u60f3\u5b9a\u3057\u3001\u6027\u8cea\u306e\u7570\u306a\u308b3\u7cfb\u5217\u3092\u4f5c\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>set.seed(2026)\nn &lt;- 100\n\n# \u7cfb\u5217A\uff1a\u5b9a\u5e38\u306aAR(1)\uff08\u30ea\u30fc\u30c9\u306b\u3064\u306a\u304c\u308c\u305f\u72ac\uff09\ne_A &lt;- arima.sim(model = list(ar = 0.5), n = n)\nseries_A &lt;- ts(10 + e_A, start = 1926)\n\n# \u7cfb\u5217B\uff1a\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\uff08\u30ea\u30fc\u30c9\u306e\u5916\u308c\u305f\u72ac\uff1d\u5358\u4f4d\u6839\uff09\nseries_B &lt;- ts(10 + cumsum(rnorm(n, mean = 0, sd = 1)), start = 1926)\n\n# \u7cfb\u5217C\uff1a\u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38\uff08\u5e740.05\u305a\u3064\u4e0a\u6607\u3059\u308b\u76f4\u7dda\uff0bAR(1)\u306e\u63fa\u3089\u304e\uff09\ne_C &lt;- arima.sim(model = list(ar = 0.5), n = n)\nseries_C &lt;- ts(10 + 0.05 * (1:n) + e_C, start = 1926)<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7cfb\u5217A\uff1a\u524d\u5e74\u306e\u5f71\u97ff\u3092\u534a\u5206\uff08$\\rho = 0.5$\uff09\u5f15\u304d\u7d99\u3050\u304c\u3001\u5e73\u574710\u306e\u307e\u308f\u308a\u306b\u623b\u3063\u3066\u304f\u308b<\/li>\n\n\n\n<li>\u7cfb\u5217B\uff1a\u524d\u5e74\u306e\u5024\u306b\u6bce\u5e74\u30e9\u30f3\u30c0\u30e0\u306a\u30b7\u30e7\u30c3\u30af\u3092\u8db3\u3057\u7d9a\u3051\u308b\uff08$\\rho = 1$\uff09<\/li>\n\n\n\n<li>\u7cfb\u5217C\uff1a100\u5e74\u30675\u5ea6\u4e0a\u304c\u308b\u76f4\u7dda\u306e\u5742\u306e\u4e0a\u3067\u3001\u7cfb\u5217A\u3068\u540c\u3058\u6027\u8cea\u306e\u63fa\u3089\u304e\u304c\u4e57\u3063\u3066\u3044\u308b<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2\uff1a\u307e\u305a\u306f\u30b0\u30e9\u30d5\u3068\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u3067\u898b\u308b<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>par(mfrow = c(3, 2))\nplot(series_A, main = \"A: Stationary AR(1)\", ylab = \"\")\nacf(series_A, main = \"ACF of A\")\nplot(series_B, main = \"B: Random walk\", ylab = \"\")\nacf(series_B, main = \"ACF of B\")\nplot(series_C, main = \"C: Trend-stationary\", ylab = \"\")\nacf(series_C, main = \"ACF of C\")\npar(mfrow = c(1, 1))<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"956\" height=\"1024\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step2-1-956x1024.png\" alt=\"\" class=\"wp-image-4841\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step2-1-956x1024.png 956w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step2-1-280x300.png 280w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step2-1-768x823.png 768w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step2-1.png 1400w\" sizes=\"(max-width: 956px) 100vw, 956px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u7cfb\u5217A<\/strong>\uff1a\u5e73\u574710\u306e\u307e\u308f\u308a\u3092\u4e0a\u4e0b\u3057\u3001\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\uff08ACF\uff09\u306f\u30e9\u30b03\u301c4\u3042\u305f\u308a\u3067\u4fe1\u983c\u533a\u9593\uff08\u9752\u3044\u70b9\u7dda\uff09\u306e\u5185\u5074\u306b\u53ce\u307e\u308b\u3002\u300c\u30ea\u30fc\u30c9\u306b\u3064\u306a\u304c\u308c\u305f\u72ac\u300d\u306e\u5178\u578b\u7684\u306a\u59ff\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u7cfb\u5217B<\/strong>\uff1a\u30b9\u30bf\u30fc\u30c8\u306f10\u5ea6\u306a\u306e\u306b\u3001\u623b\u3063\u3066\u304f\u308b\u529b\u304c\u50cd\u304b\u306a\u3044\u305f\u3081\u3001\u524d\u534a\uff081930\u5e74\u4ee3\uff09\u306b\u306f6\u5ea6\u53f0\u307e\u3067\u4e0b\u304c\u308a\u3001\u7d42\u76e4\uff082010\u5e74\u3054\u308d\uff09\u306b\u306f26\u5ea6\u53f0\u307e\u3067\u4e0a\u304c\u3063\u3066\u3044\u308b\u3002\u3053\u306e\u3088\u3046\u306b\u5e73\u5747\u306e\u4f4d\u7f6e\u306b\u623b\u3089\u305a\u3001\u3069\u3053\u3078\u5411\u304b\u3046\u304b\u6c7a\u307e\u3063\u3066\u3044\u306a\u3044\u52d5\u304d\u3092\u300c\u6f02\u6d41\u300d\u3068\u547c\u3076\u3002ACF\u3082\u30e9\u30b020\u4ed8\u8fd1\u307e\u3067\u3086\u3063\u304f\u308a\u3068\u3057\u304b\u6e1b\u8870\u3057\u306a\u3044\u3002\u3069\u3061\u3089\u3082\u5358\u4f4d\u6839\u306e\u5178\u578b\u7684\u306a\u30b5\u30a4\u30f3\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u7cfb\u5217C<\/strong>\uff1a\u53f3\u80a9\u4e0a\u304c\u308a\u3067\u3001ACF\u3082\u3086\u3063\u304f\u308a\u6e1b\u8870\u3057\u3066\u3044\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u3067\u5927\u4e8b\u306a\u306e\u306f\u3001<strong>B\u3068C\u306f\u3069\u3061\u3089\u3082\u300c\u53f3\u80a9\u4e0a\u304c\u308a\u300d\u3067\u3001ACF\u3082\u3069\u3061\u3089\u3082\u3086\u3063\u304f\u308a\u6e1b\u8870\u3059\u308b<\/strong> \u3068\u3044\u3046\u70b9\u3067\u3042\u308b\u3002\u76ee\u3067\u898b\u308b\u3060\u3051\u3067\u306f\u3001\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u3068\u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38\u3092\u533a\u5225\u3057\u306b\u304f\u3044\u3002\u3060\u304b\u3089\u691c\u5b9a\u304c\u5fc5\u8981\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3\uff1atseries\u3067\u624b\u65e9\u304f\u691c\u5b9a\u3059\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u307e\u305a\u7cfb\u5217A\u3067\u3001\u4f7f\u3044\u65b9\u3068\u51fa\u529b\u306e\u8aad\u307f\u65b9\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>adf.test(series_A)                    # H0: \u5358\u4f4d\u6839\u3042\u308a\uff08\u5b9a\u6570\u9805\uff0b\u30c8\u30ec\u30f3\u30c9\u9805\u5165\u308a\uff09\nkpss.test(series_A, null = \"Level\")   # H0: \u6c34\u6e96\u5b9a\u5e38\nkpss.test(series_A, null = \"Trend\")   # H0: \u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>\tAugmented Dickey-Fuller Test\nDickey-Fuller = -4.1429, Lag order = 4, p-value = 0.01\nalternative hypothesis: stationary\n\n\tKPSS Test for Level Stationarity\nKPSS Level = 0.12548, Truncation lag parameter = 4, p-value = 0.1\n\n\tKPSS Test for Trend Stationarity\nKPSS Trend = 0.080634, Truncation lag parameter = 4, p-value = 0.1\n\n\u8b66\u544a\u30e1\u30c3\u30bb\u30fc\u30b8:\n1: adf.test(series_A) \u3067: p-value smaller than printed p-value\n2: kpss.test(series_A, null = \"Level\") \u3067: p-value greater than printed p-value\n...<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">ADF\u691c\u5b9a\u306f\u5358\u4f4d\u6839\u3092\u68c4\u5374\u3057\u3001KPSS\u691c\u5b9a\u306f\u5b9a\u5e38\u3092\u68c4\u5374\u3057\u306a\u3044\u30022\u4eba\u306e\u88c1\u5224\u5b98\u306e\u610f\u898b\u304c\u4e00\u81f4\u3057\u3001<strong>\u7cfb\u5217A\u306f\u5b9a\u5e38<\/strong> \u3068\u5224\u5b9a\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u3067\u3001\u521d\u5b66\u8005\u304c\u3064\u307e\u305a\u304d\u3084\u3059\u3044\u70b9\u304c2\u3064\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u2460 P\u5024\u304c0.01\u30840.1\u3067\u982d\u6253\u3061\u306b\u306a\u308b<\/strong><br><code>tseries<\/code> \u306eP\u5024\u306f\u3001\u6570\u8868\u304b\u3089\u88dc\u9593\u3057\u3066\u6c42\u3081\u3066\u3044\u308b\u3002\u7d71\u8a08\u91cf\u304c\u8868\u306e\u7bc4\u56f2\u306e\u5916\u306b\u51fa\u308b\u3068\u3001P\u5024\u306f\u7bc4\u56f2\u306e\u7aef\u306e\u5024\u3067\u6b62\u307e\u308a\u3001\u8b66\u544a\u304c\u51fa\u308b\u3002\u7bc4\u56f2\u306f\u3001ADF\u306a\u30890.01\u301c0.99\u3001KPSS\u306a\u30890.01\u301c0.10\u3067\u3042\u308b\u3002&#8221;p-value smaller than printed p-value&#8221; \u306f\u300c\u672c\u5f53\u306eP\u5024\u306f0.01\u3088\u308a\u3055\u3089\u306b\u5c0f\u3055\u3044\u300d\u3068\u3044\u3046\u610f\u5473\u3067\u3001\u30a8\u30e9\u30fc\u3067\u306f\u306a\u3044\u3002\u8ad6\u6587\u306b\u306f\u300cP &lt; 0.01\u300d\u300cP &gt; 0.10\u300d\u3068\u4e0d\u7b49\u53f7\u3067\u66f8\u3051\u3070\u3088\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u2461 <code>adf.test()<\/code> \u306f\u3001\u5e38\u306b\u300c\u5b9a\u6570\u9805\uff0b\u30c8\u30ec\u30f3\u30c9\u9805\u300d\u5165\u308a\u306e\u56de\u5e30\u3067\u691c\u5b9a\u3059\u308b<\/strong><br><code>tseries::adf.test()<\/code> \u306b\u306f\u3001\u56de\u5e30\u5f0f\u306e\u578b\u3092\u9078\u3076\u5f15\u6570\u304c\u306a\u3044\u3002\u5e38\u306b\u6700\u3082\u4e00\u822c\u7684\u306a <code>\"trend\"<\/code> \u578b\u3067\u691c\u5b9a\u3059\u308b\u3002\u30c8\u30ec\u30f3\u30c9\u306e\u306a\u3044\u7cfb\u5217\u306b\u3082\u4f7f\u3048\u308b\u304c\u3001\u4e0d\u8981\u306a\u9805\u3092\u5165\u308c\u305f\u5206\u3060\u3051\u691c\u51fa\u529b\u306f\u3084\u3084\u843d\u3061\u308b\u3002\u578b\u3092\u9078\u3073\u305f\u3044\u3068\u304d\u306f\u3001\u6b21\u306e <code>urca<\/code> \u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4\uff1aurca\u3067\u578b\u3092\u660e\u793a\u3057\u3066\u691c\u5b9a\u3059\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u53f3\u80a9\u4e0a\u304c\u308a\u306e\u7cfb\u5217C\u3092\u3001<code>urca<\/code> \u3067\u8a73\u3057\u304f\u898b\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>adf_C &lt;- ur.df(series_C, type = \"trend\", lags = 4, selectlags = \"AIC\")\nsummary(adf_C)<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>Test regression trend\n...\nValue of test-statistic is: -6.487 14.2675 21.0841\n\nCritical values for test statistics:\n      1pct  5pct 10pct\ntau3 -4.04 -3.45 -3.15\nphi2  6.50  4.88  4.16\nphi3  8.73  6.49  5.47<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>lags = 4, selectlags = \"AIC\"<\/code> \u306f\u3001\u300c\u6700\u59274\u307e\u3067\u306e\u30e9\u30b0\u306e\u4e2d\u304b\u3089AIC\u3067\u6700\u9069\u306a\u3082\u306e\u3092\u9078\u3076\u300d\u3068\u3044\u3046\u6307\u5b9a\u3067\u3042\u308b<\/li>\n\n\n\n<li>\u898b\u308b\u3079\u304d\u306f <strong>\u6700\u521d\u306e\u5024\uff08tau3\uff09<\/strong> \u3067\u3042\u308b\u3002\u691c\u5b9a\u7d71\u8a08\u91cf \u22126.487 \u306f5%\u81e8\u754c\u5024 \u22123.45 \u3088\u308a\u5c0f\u3055\u3044\uff08\u3088\u308a\u30de\u30a4\u30ca\u30b9\u5074\u306b\u3042\u308b\uff09\u306e\u3067\u3001<strong>\u5358\u4f4d\u6839\u3092\u68c4\u5374<\/strong> \u3059\u308b<\/li>\n\n\n\n<li>phi2\u30fbphi3\u306f\u3001\u30c8\u30ec\u30f3\u30c9\u9805\u3084\u5b9a\u6570\u9805\u304c\u5fc5\u8981\u304b\u3069\u3046\u304b\u3092\u8abf\u3079\u308b\u305f\u3081\u306e\u691c\u5b9a\u3067\u3001\u56de\u5e30\u5f0f\u306e\u578b\u3092\u6bb5\u968e\u7684\u306b\u7d5e\u308a\u8fbc\u3080\u624b\u9806\uff08Dolado et al., 1990\uff09\u3067\u4f7f\u308f\u308c\u308b\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u5358\u4f4d\u6839\u306e\u5224\u5b9a\u306b\u76f4\u63a5\u304b\u304b\u308f\u308btau3\u3060\u3051\u3092\u898b\u308b<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u540c\u3058\u7cfb\u5217\u3067\u3082\u3001<code>adf.test()<\/code> \u306e\u7d71\u8a08\u91cf\u306f \u22123.907 \u3060\u3063\u305f\u3002\u3053\u308c\u306f <code>adf.test()<\/code> \u304c\u30e9\u30b0\u30924\u306b\u56fa\u5b9a\u3057\u3066\u3044\u308b\u306e\u306b\u5bfe\u3057\u3001\u3053\u3053\u3067\u306fAIC\u3067\u30e9\u30b01\u304c\u9078\u3070\u308c\u305f\u305f\u3081\u3067\u3042\u308b\u3002<strong>\u30e9\u30b0\u306e\u9078\u3073\u65b9\u3067\u7d71\u8a08\u91cf\u306f\u5909\u308f\u308b<\/strong> \u306e\u3067\u3001\u8ad6\u6587\u306b\u306f\u30e9\u30b0\u306e\u6c7a\u3081\u65b9\u3092\u5fc5\u305a\u66f8\u304f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7d9a\u3044\u3066KPSS\u691c\u5b9a\u3092\u30012\u3064\u306e\u578b\u3067\u5b9f\u884c\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>kpss_C_mu  &lt;- ur.kpss(series_C, type = \"mu\",  lags = \"short\")\nkpss_C_tau &lt;- ur.kpss(series_C, type = \"tau\", lags = \"short\")\nsummary(kpss_C_mu)\nsummary(kpss_C_tau)<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>Test is of type: mu with 4 lags.\nValue of test-statistic is: 1.7435\ncritical values 0.347 0.463  0.574 0.739   (10pct 5pct 2.5pct 1pct)\n\nTest is of type: tau with 4 lags.\nValue of test-statistic is: 0.1247\ncritical values 0.119 0.146  0.176 0.216   (10pct 5pct 2.5pct 1pct)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">KPSS\u691c\u5b9a\u306f\u3001\u7d71\u8a08\u91cf\u304c\u81e8\u754c\u5024\u3088\u308a <strong>\u5927\u304d\u3044<\/strong> \u3068\u304d\u306b\u68c4\u5374\u3059\u308b\uff08ADF\u3068\u306f\u5411\u304d\u304c\u9006\u3067\u3042\u308b\uff09\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>type = \"mu\"<\/code>\uff08\u6c34\u6e96\u5b9a\u5e38\uff09\uff1a1.7435 &gt; 0.463 \u2192 5%\u3067 <strong>\u5b9a\u5e38\u3092\u68c4\u5374<\/strong><\/li>\n\n\n\n<li><code>type = \"tau\"<\/code>\uff08\u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38\uff09\uff1a0.1247 &lt; 0.146 \u2192 5%\u3067 <strong>\u5b9a\u5e38\u3092\u68c4\u5374\u3057\u306a\u3044<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3064\u307e\u308a\u7cfb\u5217C\u306f\u3001\u300c\u4e00\u5b9a\u306e\u6c34\u6e96\u306e\u307e\u308f\u308a\u3067\u5b9a\u5e38\u300d\u3068\u306f\u8a00\u3048\u306a\u3044\u304c\u3001\u300c\u76f4\u7dda\u30c8\u30ec\u30f3\u30c9\u306e\u307e\u308f\u308a\u3067\u5b9a\u5e38\u300d\u3068\u306f\u8a00\u3048\u308b\u3002\u307e\u3055\u306b <strong>\u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38<\/strong> \u3068\u3044\u3046\u3001\u30c7\u30fc\u30bf\u3092\u4f5c\u3063\u305f\u3068\u304d\u306e\u8a2d\u5b9a\u3069\u304a\u308a\u306e\u7d50\u8ad6\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5\uff1a3\u7cfb\u5217\u3092\u307e\u3068\u3081\u3066\u5224\u5b9a\u8868\u306b\u5f53\u3066\u306f\u3081\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2\u3064\u306e\u691c\u5b9a\u306e\u7d50\u679c\u3092\u5224\u5b9a\u8868\u306b\u5f53\u3066\u306f\u3081\u308b\u95a2\u6570\u3092\u4f5c\u308a\u30013\u7cfb\u5217\u3092\u4e00\u6c17\u306b\u5224\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>judge &lt;- function(adf_p, kpss_p, alpha = 0.05) {\n  adf_rej  &lt;- adf_p  &lt; alpha\n  kpss_rej &lt;- kpss_p &lt; alpha\n  if ( adf_rej &amp;&amp; !kpss_rej) return(\"\u5b9a\u5e38\")\n  if (!adf_rej &amp;&amp;  kpss_rej) return(\"\u975e\u5b9a\u5e38\uff08\u5358\u4f4d\u6839\uff09\")\n  if ( adf_rej &amp;&amp;  kpss_rej) return(\"\u5224\u65ad\u4fdd\u7559\uff1a\u4e21\u65b9\u68c4\u5374\")\n  \"\u5224\u65ad\u4fdd\u7559\uff1a\u4e21\u65b9\u68c4\u5374\u305b\u305a\"\n}\n\ncheck_stationarity &lt;- function(x, kpss_null = \"Level\") {\n  adf_p  &lt;- suppressWarnings(adf.test(x)$p.value)\n  kpss_p &lt;- suppressWarnings(kpss.test(x, null = kpss_null)$p.value)\n  data.frame(ADF_p = round(adf_p, 3), KPSS_p = round(kpss_p, 3),\n             KPSS_null = kpss_null, \u5224\u5b9a = judge(adf_p, kpss_p))\n}\n\nseries_list &lt;- list(A = series_A, B = series_B, C = series_C)\nres_level &lt;- do.call(rbind, lapply(series_list, check_stationarity, kpss_null = \"Level\"))\nres_trend &lt;- do.call(rbind, lapply(series_list, check_stationarity, kpss_null = \"Trend\"))\nres_level\nres_trend<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code><code>  ADF_p KPSS_p KPSS_null             \u5224\u5b9a\nA 0.010   0.10     Level             \u5b9a\u5e38\nB 0.313   0.01     Level   \u3000\u3000\u3000\u975e\u5b9a\u5e38\uff08\u5358\u4f4d\u6839\uff09\nC 0.017   0.01     Level \u3000\u3000\u3000\u5224\u65ad\u4fdd\u7559\uff1a\u4e21\u65b9\u68c4\u5374\n\n  ADF_p KPSS_p KPSS_null             \u5224\u5b9a\nA 0.010   0.10     Trend             \u5b9a\u5e38\nB 0.313   0.01     Trend \u3000\u3000\u3000\u3000\u975e\u5b9a\u5e38\uff08\u5358\u4f4d\u6839\uff09\nC 0.017   0.09     Trend             \u5b9a\u5e38<\/code><\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8868\u306e\u5024\u306e\u610f\u5473\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b\u30020.010\u30840.01\u306f\u300c0.01\u4ee5\u4e0b\u300d\u30010.10\u306f\u300c0.10\u4ee5\u4e0a\u300d\u3092\u8868\u3059\uff08Step 3\u306e\u982d\u6253\u3061\uff09\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u7cfb\u5217A<\/strong>\uff1a\u3069\u3061\u3089\u306e\u578b\u3067\u3082\u300c\u5b9a\u5e38\u300d\u3002\u8a2d\u5b9a\u3069\u304a\u308a\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u7cfb\u5217B<\/strong>\uff1aADF\u306f\u5358\u4f4d\u6839\u3092\u68c4\u5374\u3067\u304d\u305a\uff08P = 0.313\uff09\u3001KPSS\u306f\u5b9a\u5e38\u3092\u68c4\u5374\u3057\u305f\u30022\u4eba\u306e\u610f\u898b\u304c\u300c\u975e\u5b9a\u5e38\u300d\u3067\u4e00\u81f4\u3059\u308b\u3002\u8a2d\u5b9a\u3069\u304a\u308a\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u7cfb\u5217C<\/strong>\uff1aKPSS\u3092 <strong>Level\u578b<\/strong> \u3067\u5b9f\u884c\u3059\u308b\u3068\u300c\u4e21\u65b9\u68c4\u5374\u300d\u306e\u5224\u65ad\u4fdd\u7559\u306b\u306a\u308b\u3002<strong>Trend\u578b<\/strong> \u3067\u5b9f\u884c\u3059\u308b\u3068\u300c\u5b9a\u5e38\uff08\u30c8\u30ec\u30f3\u30c9\u306e\u307e\u308f\u308a\u3067\u5b9a\u5e38\uff09\u300d\u306b\u306a\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u7cfb\u5217C\u306e\u7d50\u679c\u306f\u3001\u5224\u5b9a\u8868\u306e\u300c\u4e21\u65b9\u68c4\u5374\u300d\u304c\u4f55\u3092\u610f\u5473\u3059\u308b\u304b\u3092\u3088\u304f\u793a\u3057\u3066\u3044\u308b\u3002<code>adf.test()<\/code> \u306f\u30c8\u30ec\u30f3\u30c9\u9805\u5165\u308a\u3067\u691c\u5b9a\u3057\u3066\u3044\u308b\u306e\u306b\u3001KPSS\u3092\u300c\u6c34\u6e96\u5b9a\u5e38\u300d\u306e\u578b\u3067\u691c\u5b9a\u3057\u305f\u305f\u3081\u3001<strong>2\u4eba\u306e\u88c1\u5224\u5b98\u304c\u5225\u3005\u306e\u7f6a\u72b6\u3092\u5be9\u7406\u3057\u3066\u3044\u305f<\/strong> \u306e\u3067\u3042\u308b\u3002\u53f3\u80a9\u4e0a\u304c\u308a\u306e\u7cfb\u5217\u3067\u306f\u3001ADF\u3068KPSS\u306e\u4e21\u65b9\u3067 <strong>\u30c8\u30ec\u30f3\u30c9\u9805\u3092\u5165\u308c\u305f\u578b\u306b\u305d\u308d\u3048\u308b<\/strong> \u306e\u304c\u539f\u5247\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 6\uff1a\u5dee\u5206\u3092\u53d6\u3063\u3066\u518d\u691c\u5b9a\u3057\u3001<code>ndiffs()<\/code> \u3067\u6b21\u6570\u3092\u78ba\u304b\u3081\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u975e\u5b9a\u5e38\u3068\u5224\u5b9a\u3055\u308c\u305f\u7cfb\u5217B\u306f\u3001\u5dee\u5206\u3092\u53d6\u3063\u3066\u304b\u3089\u3082\u3046\u4e00\u5ea6\u691c\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>d_B &lt;- diff(series_B)\ncheck_stationarity(d_B, kpss_null = \"Level\")<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code><code>  ADF_p KPSS_p KPSS_null \u5224\u5b9a\n1  0.01    0.1     Level \u5b9a\u5e38<\/code><\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">1\u56de\u306e\u5dee\u5206\u3067\u5b9a\u5e38\u306b\u306a\u3063\u305f\u3002\u7cfb\u5217B\u306f\u300c1\u56de\u5dee\u5206\u3092\u53d6\u308c\u3070\u5b9a\u5e38\u306b\u306a\u308b\u7cfb\u5217\u300d\u3001\u5c02\u9580\u7528\u8a9e\u3067\u3044\u3046 <strong>I(1)\uff081\u6b21\u306e\u548c\u5206\u904e\u7a0b\uff09<\/strong> \u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><code>forecast::ndiffs()<\/code> \u3092\u4f7f\u3046\u3068\u3001\u300c\u5b9a\u5e38\u306b\u306a\u308b\u307e\u3067\u691c\u5b9a\u3068\u5dee\u5206\u3092\u7e70\u308a\u8fd4\u3059\u300d\u4f5c\u696d\u3092\u81ea\u52d5\u3067\u3084\u3063\u3066\u304f\u308c\u308b\u30023\u7cfb\u5217\u306b\u3064\u3044\u3066\u3001\u691c\u5b9a\u3068\u578b\u3092\u5909\u3048\u3066\u6bd4\u3079\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>sapply(series_list, function(x) c(\n  KPSS_level = ndiffs(x, test = \"kpss\", type = \"level\"),\n  KPSS_trend = ndiffs(x, test = \"kpss\", type = \"trend\"),\n  ADF_trend  = ndiffs(x, test = \"adf\",  type = \"trend\")\n))<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code><code>           A B C\nKPSS_level 0 1 1\nKPSS_trend 0 1 0\nADF_trend  0 1 0<\/code><\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u306b\u3082\u843d\u3068\u3057\u7a74\u304c\u3042\u308b\u3002<code>ndiffs()<\/code> \u306e\u65e2\u5b9a\u306f <strong>KPSS\u691c\u5b9a\u30fb<code>type = \"level\"<\/code><\/strong> \u3067\u3042\u308b\u3002\u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38\u306e\u7cfb\u5217C\u306b\u65e2\u5b9a\u306e\u307e\u307e\u4f7f\u3046\u3068\u3001\u300c\u5dee\u5206\u304c1\u56de\u5fc5\u8981\u300d\u3068\u5224\u5b9a\u3055\u308c\u308b\uff081\u884c\u76ee\uff09\u3002\u30c8\u30ec\u30f3\u30c9\u3092\u8003\u616e\u3057\u305f\u578b\u306b\u3059\u308b\u3068\u3001\u300c\u5dee\u5206\u306f\u4e0d\u8981\u300d\u306b\u306a\u308b\uff082\u30fb3\u884c\u76ee\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u524d\u306e\u8a18\u4e8b\u3067\u4f7f\u3063\u305f <code>auto.arima()<\/code> \u3082\u3001\u65e2\u5b9a\u3067\u306fKPSS\u691c\u5b9a\u3067\u5dee\u5206\u306e\u6b21\u6570\u3092\u6c7a\u3081\u3066\u3044\u308b\u3002\u95a2\u6570\u306b\u4efb\u305b\u304d\u308a\u306b\u305b\u305a\u3001<strong>\u30b0\u30e9\u30d5\u3092\u898b\u3066\u3001\u30c8\u30ec\u30f3\u30c9\u306e\u6709\u7121\u306b\u5408\u3063\u305f\u578b\u3092\u9078\u3076<\/strong> \u3053\u3068\u304c\u5927\u5207\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1a\u69cb\u9020\u5909\u5316\u304c\u3042\u308b\u3068\u3001\u5224\u5b9a\u3092\u8aa4\u308a\u3084\u3059\u3044<\/strong><br>\u653f\u7b56\u306e\u5c0e\u5165\u3001\u8a2d\u5099\u306e\u66f4\u65b0\u3001\u30c0\u30e0\u306e\u5efa\u8a2d\u306a\u3069\u3067\u3001\u7cfb\u5217\u306e\u6c34\u6e96\u304c <strong>\u3042\u308b\u6642\u70b9\u3067\u6bb5\u5dee\u306e\u3088\u3046\u306b\u5909\u308f\u308b<\/strong> \u3053\u3068\u304c\u3042\u308b\u3002<a href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/what-is-comparative-interrupted-time-series\/\">Comparative Interrupted Time Series\uff08CITS\uff09\u306e\u8a18\u4e8b<\/a>\u3067\u6271\u3063\u305f\u300c\u4ecb\u5165\u300d\u304c\u307e\u3055\u306b\u305d\u308c\u3067\u3042\u308b\u3002\u3053\u3046\u3057\u305f\u6bb5\u5dee\u306f\u3001ADF\u691c\u5b9a\u304b\u3089\u898b\u308b\u3068\u300c\u30b7\u30e7\u30c3\u30af\u304c\u6d88\u3048\u305a\u306b\u6b8b\u3063\u305f\u300d\u3088\u3046\u306b\u898b\u3048\u308b\u3002\u305d\u306e\u305f\u3081\u3001\u672c\u5f53\u306f <strong>\u6bb5\u5dee\u306e\u3042\u308b\u5b9a\u5e38\u7cfb\u5217<\/strong> \u3067\u3082\u300c\u5358\u4f4d\u6839\u3042\u308a\u300d\u3068\u8aa4\u5224\u5b9a\u3055\u308c\u3084\u3059\u3044\uff08Perron, 1989\uff09\u3002<br>R\u306b\u7d44\u307f\u8fbc\u307e\u308c\u3066\u3044\u308b <code>Nile<\/code>\uff08\u30ca\u30a4\u30eb\u5ddd\u306e\u5e74\u9593\u6d41\u91cf\u30011871\u301c1970\u5e74\uff09\u3067\u78ba\u304b\u3081\u3066\u307f\u3088\u3046\u3002\u3053\u306e\u7cfb\u5217\u306f\u30011898\u5e74\u3054\u308d\u306b\u6c34\u6e96\u304c\u4e0b\u304c\u3063\u305f\u3053\u3068\u3067\u77e5\u3089\u308c\u308b\uff08Cobb, 1978\uff09\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"512\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/column_nile-1-1024x512.png\" alt=\"\" class=\"wp-image-4850\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/column_nile-1-1024x512.png 1024w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/column_nile-1-300x150.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/column_nile-1-768x384.png 768w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/column_nile-1.png 1400w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>check_stationarity(Nile, kpss_null = \"Level\")\n#   ADF_p KPSS_p KPSS_null \u5224\u5b9a\n# 1 0.064   0.01     Level \u975e\u5b9a\u5e38\uff08\u5358\u4f4d\u6839\uff09<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5224\u5b9a\u8868\u3092\u305d\u306e\u307e\u307e\u5f53\u3066\u306f\u3081\u308b\u3068\u300c\u975e\u5b9a\u5e38\u300d\u306b\u306a\u308b\u3002\u3053\u3053\u3067\u3001\u5909\u5316\u70b9\u3092\u30c7\u30fc\u30bf\u304b\u3089\u63a8\u5b9a\u3057\u306a\u304c\u3089\u5358\u4f4d\u6839\u3092\u691c\u5b9a\u3059\u308b <strong>Zivot\u2013Andrews\u691c\u5b9a<\/strong>\uff08Zivot &amp; Andrews, 1992\uff09\u3092\u4f7f\u3063\u3066\u307f\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>za &lt;- ur.za(Nile, model = \"intercept\", lag = 2)   # \u30e9\u30b0\u306f\u7c21\u4fbf\u306e\u305f\u30812\u306b\u56fa\u5b9a\nsummary(za)                 # Teststatistic: -6.1751\uff085%\u81e8\u754c\u5024 -4.8\uff09\ntime(Nile)&#91;za@bpoint]       # 1898\ncheck_stationarity(window(Nile, start = 1899), kpss_null = \"Level\")\n#   ADF_p KPSS_p KPSS_null \u5224\u5b9a\n# 1  0.01    0.1     Level \u5b9a\u5e38<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u30e9\u30b0\u6b21\u6570\u306f\u3001\u672c\u6765ADF\u691c\u5b9a\u3068\u540c\u69d8\u306bAIC\u306a\u3069\u3067\u9078\u3076\u306e\u304c\u4e00\u822c\u7684\u3067\u3042\u308b\u3002\u3053\u3053\u3067\u306f\u7c21\u4fbf\u306e\u305f\u30812\u3068\u3057\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Zivot\u2013Andrews\u691c\u5b9a\u306f1898\u5e74\u306b\u5909\u5316\u70b9\u3092\u898b\u3064\u3051\u3001\u300c\u6c34\u6e96\u306e\u6bb5\u5dee\u30921\u56de\u8a31\u305b\u3070\u5358\u4f4d\u6839\u306f\u68c4\u5374\u3055\u308c\u308b\u300d\u3068\u5224\u5b9a\u3057\u305f\u3002\u5b9f\u969b\u30011899\u5e74\u4ee5\u964d\u3060\u3051\u3067\u691c\u5b9a\u3057\u76f4\u3059\u3068\u300c\u5b9a\u5e38\u300d\u306b\u306a\u308b\u3002<br>\u4ecb\u5165\u306e\u52b9\u679c\u3092\u8abf\u3079\u308b\u5206\u5272\u6642\u7cfb\u5217\uff08ITS\uff09\u89e3\u6790\u3067\u306f\u3001\u3053\u306e\u70b9\u304c\u7279\u306b\u91cd\u8981\u3067\u3042\u308b\u3002\u4ecb\u5165\u3092\u307e\u305f\u3044\u3060\u7cfb\u5217\u5168\u4f53\u306b\u5358\u4f4d\u6839\u691c\u5b9a\u3092\u4f7f\u3046\u3068\u3001\u4ecb\u5165\u52b9\u679c\u305d\u306e\u3082\u306e\u3092\u300c\u5358\u4f4d\u6839\u300d\u3068\u53d6\u308a\u9055\u3048\u308b\u304a\u305d\u308c\u304c\u3042\u308b\u3002<strong>\u4ecb\u5165\u524d\u306e\u671f\u9593\u3060\u3051\u3067\u691c\u5b9a\u3059\u308b<\/strong>\u3001\u3042\u308b\u3044\u306f\u5909\u5316\u70b9\u3092\u8003\u616e\u3057\u305f\u691c\u5b9a\u3092\u4f7f\u3046\u306e\u304c\u5b89\u5168\u3067\u3042\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">\u3069\u3046\u4f7f\u3044\u5206\u3051\u308b\u304b\uff1a\u5224\u65ad\u306e\u6d41\u308c<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u30b0\u30e9\u30d5\u3068ACF\u3092\u898b\u308b<\/strong>\uff1a\u30c8\u30ec\u30f3\u30c9\u306e\u6709\u7121\u3001\u6bb5\u5dee\uff08\u69cb\u9020\u5909\u5316\uff09\u306e\u6709\u7121\u3001\u5b63\u7bc0\u6027\u306e\u6709\u7121\u3092\u78ba\u8a8d\u3059\u308b<\/li>\n\n\n\n<li><strong>\u578b\u3092\u6c7a\u3081\u308b<\/strong>\uff1a\u30c8\u30ec\u30f3\u30c9\u304c\u3042\u308c\u3070ADF\u306f <code>\"trend\"<\/code> \u578b\u3001KPSS\u306f <code>\"Trend\"<\/code>\uff0f<code>\"tau\"<\/code> \u578b\u3002\u306a\u3051\u308c\u3070 <code>\"drift\"<\/code> \u578b\u3068 <code>\"Level\"<\/code>\uff0f<code>\"mu\"<\/code> \u578b<\/li>\n\n\n\n<li><strong>ADF\u3068KPSS\u3092\u4e21\u65b9\u5b9f\u884c<\/strong> \u3057\u3001\u5224\u5b9a\u8868\u3067\u8aad\u3080<\/li>\n\n\n\n<li><strong>\u300c\u975e\u5b9a\u5e38\u300d\u306a\u3089\u5dee\u5206\u3092\u53d6\u308a\u3001\u518d\u30733\u3078<\/strong>\u3002<code>ndiffs()<\/code> \u306e\u7d50\u679c\u3068\u7167\u3089\u3057\u5408\u308f\u305b\u308b<\/li>\n\n\n\n<li><strong>\u5224\u65ad\u4fdd\u7559\u306a\u3089\u7acb\u3061\u6b62\u307e\u308b<\/strong>\uff1a\u578b\u306e\u6307\u5b9a\u3001\u69cb\u9020\u5909\u5316\uff08Zivot\u2013Andrews\u691c\u5b9a\u30fb\u4ecb\u5165\u524d\u3060\u3051\u3067\u306e\u691c\u5b9a\uff09\u3001\u30c7\u30fc\u30bf\u306e\u9577\u3055\u3092\u898b\u76f4\u3059<\/li>\n\n\n\n<li><strong>\u6708\u6b21\u30fb\u56db\u534a\u671f\u30c7\u30fc\u30bf\u306a\u3089\u5b63\u7bc0\u6027\u3082\u78ba\u304b\u3081\u308b<\/strong>\uff1a<code>forecast::nsdiffs()<\/code> \u3067\u5b63\u7bc0\u5dee\u5206\uff08\u6708\u6b21\u306a\u308912\u304b\u6708\u524d\u3068\u306e\u5dee\uff09\u304c\u5fc5\u8981\u304b\u3092\u78ba\u304b\u3081\u308b\u3002\u5b63\u7bc0\u5dee\u5206\u3092\u53d6\u308b\u3068\u3001\u6700\u521d\u306e12\u70b9\uff08\u6708\u6b21\u306e\u5834\u5408\uff09\u304c\u5931\u308f\u308c\u308b\u3002\u305d\u306e\u305f\u3081\u3001\u7cfb\u5217\u306b\u306f\u5341\u5206\u306a\u9577\u3055\u304c\u5fc5\u8981\u306b\u306a\u308b\uff08Schaffer et al., 2021\uff09<\/li>\n<\/ol>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1a\u691c\u5b9a\u3092\u91cd\u306d\u308b\u3053\u3068\u306e\u6ce8\u610f<\/strong><br>ADF\u3068KPSS\u3092\u305d\u308c\u305e\u308c\u6709\u610f\u6c34\u6e965%\u3067\u5b9f\u884c\u3057\u3001\u5dee\u5206\u3092\u53d6\u3063\u305f\u3042\u3068\u306b\u3082\u691c\u5b9a\u3092\u7e70\u308a\u8fd4\u3059\u3068\u3001\u624b\u9806\u5168\u4f53\u3068\u3057\u3066\u300c\u8aa4\u3063\u305f\u5224\u5b9a\u3092\u3059\u308b\u78ba\u7387\u300d\u306f\u3001\u540d\u76ee\u306e5%\u3068\u306f\u4e00\u81f4\u3057\u306a\u304f\u306a\u308b\u3002\u691c\u5b9a\u3092\u91cd\u306d\u308b\u307b\u3069\u3001\u3069\u3053\u304b\u3067\u8aa4\u308b\u6a5f\u4f1a\u304c\u5897\u3048\u308b\u304b\u3089\u3067\u3042\u308b\u3002\u5358\u4f4d\u6839\u691c\u5b9a\u306e\u7d50\u679c\u306f\u300c\u7d76\u5bfe\u306e\u5224\u6c7a\u300d\u3067\u306f\u306a\u304f\u3001\u30b0\u30e9\u30d5\u30fbACF\u30fb\u5206\u91ce\u306e\u77e5\u8b58\u3068\u5408\u308f\u305b\u3066\u3001\u30e2\u30c7\u30eb\u3092\u9078\u3076\u305f\u3081\u306e <strong>\u5224\u65ad\u6750\u6599\u306e\u4e00\u3064<\/strong> \u3068\u3057\u3066\u6271\u3046\u306e\u304c\u5065\u5168\u3067\u3042\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">4. \u8ad6\u6587\u3067\u305d\u306e\u307e\u307e\u4f7f\u3048\u308b\u82f1\u6587\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u306e\u6570\u5024\u306f\u3001\u672c\u8a18\u4e8b\u306e\u7591\u4f3c\u30c7\u30fc\u30bf\uff08\u7cfb\u5217C\uff09\u3068 <code>Nile<\/code> \u3092\u5b9f\u969b\u306b\u89e3\u6790\u3057\u305f\u7d50\u679c\u3067\u3042\u308b\u3002\u81ea\u5206\u306e\u30c7\u30fc\u30bf\u306b\u4f7f\u3046\u3068\u304d\u306f\u3001\u5fc5\u305a\u81ea\u5206\u306e\u89e3\u6790\u7d50\u679c\u306b\u7f6e\u304d\u63db\u3048\u3066\u307b\u3057\u3044\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Methods<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Stationarity of each time series was assessed using two complementary tests with opposite null hypotheses: the augmented Dickey\u2013Fuller (ADF) test, whose null hypothesis is the presence of a unit root, and the Kwiatkowski\u2013Phillips\u2013Schmidt\u2013Shin (KPSS) test, whose null hypothesis is stationarity. For series with a visible trend, both tests included a constant and a linear trend; otherwise, only a constant was included. The lag order of the ADF regression was selected by the Akaike information criterion (maximum of 4 lags), and the KPSS test used the short bandwidth, trunc(4(n\/100)^(1\/4)). A series was considered stationary when the ADF test rejected and the KPSS test did not reject their respective null hypotheses at the 5% significance level, and non-stationary when the reverse was observed. Series judged to be non-stationary were first-differenced and re-tested. When the results were inconclusive or a structural break was suspected on visual inspection, the possibility of a structural break was examined using the Zivot\u2013Andrews test. All analyses were performed in R version 4.6.1 using the tseries, urca, and forecast packages.<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\uff08\u548c\u8a33\u306e\u8981\u70b9\uff1aADF\u3068KPSS\u306e2\u3064\u3092\u4f7f\u3063\u305f\u3053\u3068\u3001\u30c8\u30ec\u30f3\u30c9\u306e\u6709\u7121\u3067\u578b\u3092\u5909\u3048\u305f\u3053\u3068\u3001\u30e9\u30b0\u306e\u6c7a\u3081\u65b9\u3001\u5b9a\u5e38\u30fb\u975e\u5b9a\u5e38\u306e\u5224\u5b9a\u30eb\u30fc\u30eb\u3001\u975e\u5b9a\u5e38\u306a\u3089\u5dee\u5206\u3092\u53d6\u308b\u3053\u3068\u3001\u98df\u3044\u9055\u3063\u305f\u3068\u304d\u306fZivot\u2013Andrews\u691c\u5b9a\u3067\u69cb\u9020\u5909\u5316\u3092\u8abf\u3079\u305f\u3053\u3068\uff09<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Results<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">The ADF test rejected the null hypothesis of a unit root (\u03c4 = \u22126.49; 5% critical value, \u22123.45), whereas the KPSS test did not reject the null hypothesis of trend stationarity (KPSS statistic = 0.125; 5% critical value, 0.146). The series was therefore considered trend-stationary, and no differencing was applied.<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\u69cb\u9020\u5909\u5316\u3092\u6271\u3063\u305f\u5834\u5408\u306e\u8a18\u8ff0\u4f8b\uff1a<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">For the annual flow series, the ADF test did not reject the unit root null hypothesis (P = 0.064), and the KPSS test rejected the null hypothesis of level stationarity (P &lt; 0.01). However, the Zivot\u2013Andrews test identified a structural break in the level in 1898 and rejected the unit root null hypothesis (test statistic = \u22126.18; 5% critical value, \u22124.80). When restricted to the post-break period (1899\u20131970), the series was stationary according to both tests (ADF, P &lt; 0.01; KPSS, P &gt; 0.10).<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u67fb\u8aad\u8005\u306b\u300c\u306a\u305c2\u3064\u306e\u691c\u5b9a\u3092\u4f7f\u3063\u305f\u306e\u304b\u300d\u3068\u805e\u304b\u308c\u305f\u3068\u304d\u306e\u4e00\u6587<\/strong><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Because unit root tests such as the ADF test have limited power to distinguish a unit root from a highly persistent stationary process, particularly in short series, we used the KPSS test as a confirmatory test with the reverse null hypothesis.<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u307e\u3068\u3081<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5b9a\u5e38<\/strong> \u306f\u300c\u30ea\u30fc\u30c9\u306b\u3064\u306a\u304c\u308c\u305f\u72ac\u300d\u3001<strong>\u5358\u4f4d\u6839<\/strong> \u306f\u300c\u30b7\u30e7\u30c3\u30af\u306e\u8a18\u61b6\u304c\u6d88\u3048\u306a\u3044\uff08\u6c34\u4f4d\u304c\u4e0a\u304c\u3063\u305f\u307e\u307e\u306e\u6c60\uff09\u300d\u7cfb\u5217\u3067\u3042\u308b\u3002\u975e\u5b9a\u5e38\u306a\u7cfb\u5217\u3092\u305d\u306e\u307e\u307e\u56de\u5e30\u3059\u308b\u3068\u3001\u898b\u305b\u304b\u3051\u306e\u95a2\u9023\u304c\u51fa\u308b\u3002<\/li>\n\n\n\n<li><strong>ADF\uff08H0\uff1a\u5358\u4f4d\u6839\uff09<\/strong> \u3068 <strong>KPSS\uff08H0\uff1a\u5b9a\u5e38\uff09<\/strong> \u306f\u5e30\u7121\u4eee\u8aac\u304c\u9006\u3067\u3042\u308b\u3002\u7247\u65b9\u306e\u300c\u68c4\u5374\u3067\u304d\u306a\u3044\u300d\u3060\u3051\u3067\u306f\u4f55\u3082\u8a3c\u660e\u3055\u308c\u306a\u3044\u306e\u3067\u3001<strong>2\u3064\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u5224\u5b9a\u8868<\/strong> \u3067\u8aad\u3080\u3002<\/li>\n\n\n\n<li><strong>\u30c8\u30ec\u30f3\u30c9\u306e\u578b\u3092\u305d\u308d\u3048\u308b<\/strong>\u3002\u53f3\u80a9\u4e0a\u304c\u308a\u306e\u7cfb\u5217\u3067\u578b\u3092\u53d6\u308a\u9055\u3048\u308b\u3068\u3001\u300c\u4e21\u65b9\u68c4\u5374\u300d\u306e\u5224\u65ad\u4fdd\u7559\u3084\u3001\u4e0d\u8981\u306a\u5dee\u5206\uff08<code>ndiffs()<\/code> \u306e\u65e2\u5b9a\uff09\u306b\u3064\u306a\u304c\u308b\u3002<\/li>\n\n\n\n<li><strong>\u69cb\u9020\u5909\u5316\uff08\u4ecb\u5165\uff09<\/strong> \u306f\u5358\u4f4d\u6839\u3068\u898b\u5206\u3051\u306b\u304f\u3044\u3002\u5224\u5b9a\u304c\u98df\u3044\u9055\u3063\u305f\u3089\u3001Zivot\u2013Andrews\u691c\u5b9a\u3084\u3001\u4ecb\u5165\u524d\u306e\u671f\u9593\u3060\u3051\u3067\u306e\u691c\u5b9a\u3092\u8a66\u3059\u3002<\/li>\n\n\n\n<li>\u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38\u3068\u78ba\u304b\u3081\u305f\u3046\u3048\u3067\u300c\u3069\u308c\u304f\u3089\u3044\u5897\u3048\u3066\u3044\u308b\u304b\u300d\u3092\u8a9e\u308b\u306b\u306f\u3001Mann-Kendall\u691c\u5b9a\u3068Sen&#8217;s slope\u304c\u4f7f\u3048\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e00\u62ec\u30b3\u30d4\u30da\u7528R\u30b9\u30af\u30ea\u30d7\u30c8<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code># ============================================================\n# ADF\u691c\u5b9a\u3068KPSS\u691c\u5b9a\u306b\u3088\u308b\u6642\u7cfb\u5217\u306e\u5b9a\u5e38\u6027\u5224\u5b9a\n# ============================================================\n\n# --- \u30d1\u30c3\u30b1\u30fc\u30b8 ---\n# install.packages(c(\"tseries\", \"urca\", \"forecast\"))\nlibrary(tseries)\nlibrary(urca)\nlibrary(forecast)\n\n# --- Step 1\uff1a\u7591\u4f3c\u30c7\u30fc\u30bf\u306e\u4f5c\u6210\uff081926\u301c2025\u5e74\u306e\u5e74\u6b21\u30c7\u30fc\u30bf\u3001100\u70b9\uff09---\nset.seed(2026)\nn &lt;- 100\n\n# \u7cfb\u5217A\uff1a\u5b9a\u5e38\u306aAR(1)\uff08\u30ea\u30fc\u30c9\u306b\u3064\u306a\u304c\u308c\u305f\u72ac\uff09\ne_A &lt;- arima.sim(model = list(ar = 0.5), n = n)\nseries_A &lt;- ts(10 + e_A, start = 1926)\n\n# \u7cfb\u5217B\uff1a\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\uff08\u30ea\u30fc\u30c9\u306e\u5916\u308c\u305f\u72ac\uff1d\u5358\u4f4d\u6839\uff09\nseries_B &lt;- ts(10 + cumsum(rnorm(n, mean = 0, sd = 1)), start = 1926)\n\n# \u7cfb\u5217C\uff1a\u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38\uff08\u5e740.05\u305a\u3064\u4e0a\u6607\u3059\u308b\u76f4\u7dda\uff0bAR(1)\u306e\u63fa\u3089\u304e\uff09\ne_C &lt;- arima.sim(model = list(ar = 0.5), n = n)\nseries_C &lt;- ts(10 + 0.05 * (1:n) + e_C, start = 1926)\n\n# --- Step 2\uff1a\u30b0\u30e9\u30d5\u3068\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0 ---\npar(mfrow = c(3, 2))\nplot(series_A, main = \"A: Stationary AR(1)\", ylab = \"\")\nacf(series_A, main = \"ACF of A\")\nplot(series_B, main = \"B: Random walk\", ylab = \"\")\nacf(series_B, main = \"ACF of B\")\nplot(series_C, main = \"C: Trend-stationary\", ylab = \"\")\nacf(series_C, main = \"ACF of C\")\npar(mfrow = c(1, 1))\n\n# --- Step 3\uff1atseries\u3067\u624b\u65e9\u304f\u691c\u5b9a ---\nadf.test(series_A)                    # H0: \u5358\u4f4d\u6839\u3042\u308a\uff08\u5b9a\u6570\u9805\uff0b\u30c8\u30ec\u30f3\u30c9\u9805\u5165\u308a\uff09\nkpss.test(series_A, null = \"Level\")   # H0: \u6c34\u6e96\u5b9a\u5e38\nkpss.test(series_A, null = \"Trend\")   # H0: \u30c8\u30ec\u30f3\u30c9\u5b9a\u5e38\n\n# --- Step 4\uff1aurca\u3067\u578b\u3092\u660e\u793a\u3057\u3066\u691c\u5b9a ---\nadf_C &lt;- ur.df(series_C, type = \"trend\", lags = 4, selectlags = \"AIC\")\nsummary(adf_C)\nkpss_C_mu  &lt;- ur.kpss(series_C, type = \"mu\",  lags = \"short\")\nkpss_C_tau &lt;- ur.kpss(series_C, type = \"tau\", lags = \"short\")\nsummary(kpss_C_mu)\nsummary(kpss_C_tau)\n\n# --- Step 5\uff1aADF\u00d7KPSS\u306e\u5224\u5b9a\u8868\u3092\u4e00\u62ec\u4f5c\u6210 ---\njudge &lt;- function(adf_p, kpss_p, alpha = 0.05) {\n  adf_rej  &lt;- adf_p  &lt; alpha\n  kpss_rej &lt;- kpss_p &lt; alpha\n  if ( adf_rej &amp;&amp; !kpss_rej) return(\"\u5b9a\u5e38\")\n  if (!adf_rej &amp;&amp;  kpss_rej) return(\"\u975e\u5b9a\u5e38\uff08\u5358\u4f4d\u6839\uff09\")\n  if ( adf_rej &amp;&amp;  kpss_rej) return(\"\u5224\u65ad\u4fdd\u7559\uff1a\u4e21\u65b9\u68c4\u5374\")\n  \"\u5224\u65ad\u4fdd\u7559\uff1a\u4e21\u65b9\u68c4\u5374\u305b\u305a\"\n}\n\ncheck_stationarity &lt;- function(x, kpss_null = \"Level\") {\n  adf_p  &lt;- suppressWarnings(adf.test(x)$p.value)\n  kpss_p &lt;- suppressWarnings(kpss.test(x, null = kpss_null)$p.value)\n  data.frame(ADF_p = round(adf_p, 3), KPSS_p = round(kpss_p, 3),\n             KPSS_null = kpss_null, \u5224\u5b9a = judge(adf_p, kpss_p))\n}\n\nseries_list &lt;- list(A = series_A, B = series_B, C = series_C)\nres_level &lt;- do.call(rbind, lapply(series_list, check_stationarity, kpss_null = \"Level\"))\nres_trend &lt;- do.call(rbind, lapply(series_list, check_stationarity, kpss_null = \"Trend\"))\nres_level\nres_trend\n\n# --- Step 6\uff1a\u5dee\u5206\u3092\u53d6\u3063\u3066\u518d\u691c\u5b9a\u3057\u3001ndiffs()\u3067\u6b21\u6570\u3092\u78ba\u8a8d ---\nd_B &lt;- diff(series_B)\ncheck_stationarity(d_B, kpss_null = \"Level\")\n\nsapply(series_list, function(x) c(\n  KPSS_level = ndiffs(x, test = \"kpss\", type = \"level\"),\n  KPSS_trend = ndiffs(x, test = \"kpss\", type = \"trend\"),\n  ADF_trend  = ndiffs(x, test = \"adf\",  type = \"trend\")\n))\n\n# --- \u30b3\u30e9\u30e0\uff1a\u69cb\u9020\u5909\u5316\uff08\u30ca\u30a4\u30eb\u5ddd\u306e\u5e74\u9593\u6d41\u91cf Nile\uff09---\nplot(Nile, main = \"Nile river flow (1871-1970)\", ylab = \"\")\ncheck_stationarity(Nile, kpss_null = \"Level\")\nza &lt;- ur.za(Nile, model = \"intercept\", lag = 2)   # \u30e9\u30b0\u306f\u7c21\u4fbf\u306e\u305f\u30812\u306b\u56fa\u5b9a\nsummary(za)\ntime(Nile)&#91;za@bpoint]                 # \u63a8\u5b9a\u3055\u308c\u305f\u5909\u5316\u70b9\u306e\u5e74\ncheck_stationarity(window(Nile, start = 1899), kpss_null = \"Level\")<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u95a2\u9023\u8a18\u4e8b<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/basics-of-time-series-analysis\/\">R\u3067\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u5206\u6790\u3092\u884c\u3046\u65b9\u6cd5<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-test-whether-a-time-series-is-increasing-in-r-mann-kendall-test-and-sens-slope\/\">\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u306e\u300c\u5897\u3048\u3066\u3044\u308b\u300d\u3092R\u3067\u5224\u5b9a\u3059\u308b\u65b9\u6cd5\uff5cMann-Kendall\u691c\u5b9a\u3068Sen&#8217;s slope<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/what-is-comparative-interrupted-time-series\/\">Comparative Interrupted Time Series \u3068\u306f\u4f55\u304b \u3069\u3093\u306a\u6642\u306b\u4f7f\u3046\u306e\u304c\u826f\u3044\u304b \u308f\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac<\/a><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u53c2\u8003\u6587\u732e<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Dickey DA, Fuller WA. Distribution of the estimators for autoregressive time series with a unit root. <em>Journal of the American Statistical Association<\/em>. 1979;74(366a):427\u2013431. <a href=\"https:\/\/doi.org\/10.1080\/01621459.1979.10482531\">https:\/\/doi.org\/10.1080\/01621459.1979.10482531<\/a><\/li>\n\n\n\n<li>Said SE, Dickey DA. Testing for unit roots in autoregressive-moving average models of unknown order. <em>Biometrika<\/em>. 1984;71(3):599\u2013607. <a href=\"https:\/\/academic.oup.com\/biomet\/article-abstract\/71\/3\/599\/258758\">https:\/\/academic.oup.com\/biomet\/article-abstract\/71\/3\/599\/258758<\/a><\/li>\n\n\n\n<li>Kwiatkowski D, Phillips PCB, Schmidt P, Shin Y. Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? <em>Journal of Econometrics<\/em>. 1992;54(1\u20133):159\u2013178. <a href=\"https:\/\/ideas.repec.org\/a\/eee\/econom\/v54y1992i1-3p159-178.html\">https:\/\/ideas.repec.org\/a\/eee\/econom\/v54y1992i1-3p159-178.html<\/a><\/li>\n\n\n\n<li>Granger CWJ, Newbold P. Spurious regressions in econometrics. <em>Journal of Econometrics<\/em>. 1974;2(2):111\u2013120. <a href=\"https:\/\/ideas.repec.org\/a\/eee\/econom\/v2y1974i2p111-120.html\">https:\/\/ideas.repec.org\/a\/eee\/econom\/v2y1974i2p111-120.html<\/a><\/li>\n\n\n\n<li>Perron P. The great crash, the oil price shock, and the unit root hypothesis. <em>Econometrica<\/em>. 1989;57(6):1361\u20131401. <a href=\"https:\/\/www.jstor.org\/stable\/1913712\">https:\/\/www.jstor.org\/stable\/1913712<\/a><\/li>\n\n\n\n<li>Zivot E, Andrews DWK. Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. <em>Journal of Business &amp; Economic Statistics<\/em>. 1992;10(3):251\u2013270. <a href=\"https:\/\/doi.org\/10.1080\/07350015.1992.10509904\">https:\/\/doi.org\/10.1080\/07350015.1992.10509904<\/a><\/li>\n\n\n\n<li>Cobb GW. The problem of the Nile: Conditional solution to a changepoint problem. <em>Biometrika<\/em>. 1978;65(2):243\u2013251. <a href=\"https:\/\/doi.org\/10.1093\/biomet\/65.2.243\">https:\/\/doi.org\/10.1093\/biomet\/65.2.243<\/a><\/li>\n\n\n\n<li>Pan H, Liu J, Li F, et al. Improving influenza prediction in Quanzhou, China: an ARIMAX model integrated with meteorological drivers. <em>Frontiers in Public Health<\/em>. 2025;13:1662775. <a href=\"https:\/\/doi.org\/10.3389\/fpubh.2025.1662775\">https:\/\/doi.org\/10.3389\/fpubh.2025.1662775<\/a><\/li>\n\n\n\n<li>Hyndman RJ, Athanasopoulos G. <em>Forecasting: Principles and Practice<\/em>, 3rd ed. 9.1 Stationarity and differencing. <a href=\"https:\/\/otexts.com\/fpp3\/stationarity.html\">https:\/\/otexts.com\/fpp3\/stationarity.html<\/a><\/li>\n\n\n\n<li>Nelson CR, Plosser CI. Trends and random walks in macroeconomic time series: Some evidence and implications. <em>Journal of Monetary Economics<\/em>. 1982;10(2):139\u2013162. <a href=\"https:\/\/ideas.repec.org\/a\/eee\/moneco\/v10y1982i2p139-162.html\">https:\/\/ideas.repec.org\/a\/eee\/moneco\/v10y1982i2p139-162.html<\/a><\/li>\n\n\n\n<li>Dolado JJ, Jenkinson T, Sosvilla-Rivero S. Cointegration and unit roots. <em>Journal of Economic Surveys<\/em>. 1990;4(3):249\u2013273. <a href=\"https:\/\/doi.org\/10.1111\/j.1467-6419.1990.tb00088.x\">https:\/\/doi.org\/10.1111\/j.1467-6419.1990.tb00088.x<\/a><\/li>\n\n\n\n<li>Schaffer AL, Dobbins TA, Pearson SA. Interrupted time series analysis using autoregressive integrated moving average (ARIMA) models: a guide for evaluating large-scale health interventions. <em>BMC Medical Research Methodology<\/em>. 2021;21:58. <a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/33752604\/\">https:\/\/pubmed.ncbi.nlm.nih.gov\/33752604\/<\/a><\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u304a\u3059\u3059\u3081\u66f8\u7c4d<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5358\u4f4d\u6839\u691c\u5b9a\u3092\u3082\u3046\u4e00\u6b69\u6df1\u304f\u5b66\u3073\u305f\u3044\u4eba\u5411\u3051\u306b\u3001\u7406\u8ad6\u306e\u5b9a\u756a\u66f8\u3001R\u3067\u5b9f\u88c5\u3059\u308b\u5165\u9580\u66f8\u3001\u672c\u8a18\u4e8b\u3067\u4f7f\u3063\u305f <code>urca<\/code> \u306e\u4f5c\u8005\u306b\u3088\u308b\u89e3\u8aac\u66f8\u3001\u7121\u6599\u3067\u8aad\u3081\u308b\u5b9f\u8df5\u7684\u306a\u6559\u79d1\u66f8\u3092\u7d39\u4ecb\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. \u6c96\u672c\u7adc\u7fa9\u300e\u7d4c\u6e08\u30fb\u30d5\u30a1\u30a4\u30ca\u30f3\u30b9\u30c7\u30fc\u30bf\u306e\u8a08\u91cf\u6642\u7cfb\u5217\u5206\u6790\u300f\uff08\u7d71\u8a08\u30e9\u30a4\u30d6\u30e9\u30ea\u30fc, \u671d\u5009\u66f8\u5e97\uff09<\/strong><br>\u5358\u4f4d\u6839\u904e\u7a0b\u3068\u5358\u4f4d\u6839\u691c\u5b9a\u3092\u6b63\u9762\u304b\u3089\u6271\u3046\u5b9a\u756a\u66f8\u3067\u3042\u308b\u3002\u672c\u8a18\u4e8b\u3067\u6bd4\u55a9\u3092\u4f7f\u3063\u3066\u8aac\u660e\u3057\u305f\u300c\u5b9a\u5e38\u300d\u300c\u5358\u4f4d\u6839\u300d\u300c\u898b\u305b\u304b\u3051\u306e\u56de\u5e30\u300d\u3092\u3001\u6570\u5f0f\u3067\u304d\u3061\u3093\u3068\u7406\u89e3\u3057\u305f\u3044\u4eba\u306b\u5411\u3044\u3066\u3044\u308b\u3002<br>&#x1f449; <a href=\"https:\/\/amzn.to\/4yaADPQ\">https:\/\/www.amazon.co.jp\/dp\/4254127928<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. \u99ac\u5834\u771f\u54c9\u300e\u6642\u7cfb\u5217\u5206\u6790\u3068\u72b6\u614b\u7a7a\u9593\u30e2\u30c7\u30eb\u306e\u57fa\u790e\uff1aR\u3068Stan\u3067\u5b66\u3076\u7406\u8ad6\u3068\u5b9f\u88c5\u300f\uff08\u30d7\u30ec\u30a2\u30c7\u30b9\u51fa\u7248\uff09<\/strong><br>\u81ea\u5df1\u76f8\u95a2\u3001\u5dee\u5206\u3001ARIMA\u3068\u3044\u3063\u305f\u6642\u7cfb\u5217\u5206\u6790\u306e\u57fa\u672c\u3092\u3001R\u306e\u30b3\u30fc\u30c9\u3068\u3068\u3082\u306b\u4e00\u304b\u3089\u5b66\u3079\u308b\u3002\u6570\u5f0f\u306b\u82e6\u624b\u610f\u8b58\u304c\u3042\u308b\u4eba\u306e\u6700\u521d\u306e1\u518a\u3068\u3057\u3066\u6700\u9069\u3067\u3042\u308b\u3002<br>&#x1f449; <a href=\"https:\/\/amzn.to\/3Vc3lRS\">https:\/\/www.amazon.co.jp\/dp\/4903814874<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. Pfaff B. <em>Analysis of Integrated and Cointegrated Time Series with R<\/em>, 2nd ed.\uff08Springer, Use R! \u30b7\u30ea\u30fc\u30ba, 2008\uff09<\/strong><br>\u672c\u8a18\u4e8b\u3067\u4f7f\u3063\u305f <code>urca<\/code> \u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u4f5c\u8005\u81ea\u8eab\u306b\u3088\u308b\u89e3\u8aac\u66f8\u3067\u3042\u308b\u3002<code>ur.df()<\/code>\u30fb<code>ur.kpss()<\/code>\u30fb<code>ur.za()<\/code> \u306e\u7406\u8ad6\u3068\u4f7f\u3044\u65b9\u3092\u8a73\u3057\u304f\u5b66\u3079\u308b\u3002<br>&#x1f449; <a href=\"https:\/\/www.amazon.com\/dp\/0387759662\">https:\/\/www.amazon.com\/dp\/0387759662<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4. Hyndman RJ, Athanasopoulos G. <em>Forecasting: Principles and Practice<\/em>, 3rd ed.\uff08\u7121\u6599\u306eWeb\u7248\uff09<\/strong><br>\u5dee\u5206\u3001KPSS\u691c\u5b9a\u3001\u5b63\u7bc0\u5dee\u5206\u3001ARIMA\u3092\u3001\u5b9f\u30c7\u30fc\u30bf\u3067\u5b9f\u8df5\u7684\u306b\u5b66\u3079\u308b\u6559\u79d1\u66f8\u3067\u3042\u308b\u3002Web\u4e0a\u3067\u7121\u6599\u3067\u5168\u6587\u3092\u8aad\u3081\u308b\u3002<br>&#x1f449; <a href=\"https:\/\/otexts.com\/fpp3\/\">https:\/\/otexts.com\/fpp3\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5f8c\u8f29\uff1a\u300c\u5148\u8f29\u3001\u3053\u306e\u524d\u6559\u308f\u3063\u305fMann-Kendall\u691c\u5b9a\u3092\u3001\u3042\u308b\u5730\u70b9\u306e\u5e74\u5e73\u5747\u6c17\u6e29100\u5e74\u5206\u306b\u4f7f\u3063\u3066\u307f\u305f\u3093\u3067\u3059\u3002P &lt; 0.05\u3067\u3001\u3057\u3063\u304b\u308a\u300e\u5897\u3048\u3066\u3044\u308b\u300f\u3068\u51fa\u307e\u3057\u305f\uff01\u300d \u5148\u8f29\uff1a\u300c\u30b0\u30e9\u30d5\u306f\u898b\u305f\u304b\u3044\uff1f\u300d \u5f8c\u8f29\uff1a\u300c\u306f\u3044\u3001\u53f3 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":4853,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[54],"tags":[],"class_list":["post-4839","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-54"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/ADF_KPSS-scaled.jpeg","_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4839","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/comments?post=4839"}],"version-history":[{"count":10,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4839\/revisions"}],"predecessor-version":[{"id":4852,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4839\/revisions\/4852"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/4853"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=4839"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=4839"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=4839"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}