{"id":10822,"date":"2026-09-22T06:00:00","date_gmt":"2026-09-21T21:00:00","guid":{"rendered":"https:\/\/triumphmind.com\/cfa\/2026\/09\/22\/cfa-l2-quants-lm5\/"},"modified":"2026-09-22T07:05:31","modified_gmt":"2026-09-21T22:05:31","slug":"cfa-l2-quants-lm5","status":"publish","type":"post","link":"https:\/\/triumphmind.com\/cfa\/2026\/09\/22\/cfa-l2-quants-lm5\/","title":{"rendered":"\u3010CFA\u00ae\ufe0e L2 Quants LM5\u3011Time-Series Analysis \u3092\u8981\u70b9\u89e3\u8aac\uff5c\u30c8\u30ec\u30f3\u30c9\u30fb\u30e2\u30c7\u30eb\u30fbAR\u30e2\u30c7\u30eb\u30fb\u5358\u4f4d\u6839\u30fb\u5b63\u7bc0\u6027\u30fbARCH"},"content":{"rendered":"<style>\n.cfalm-los{counter-reset:los;list-style:none;padding:0!important;margin:1em 0!important}\n.cfalm-los li{border:1px solid #d5d9e3;border-left:4px solid #172152;border-radius:4px;padding:.8em 1em!important;margin:0 0 .8em!important;background:#fff}\n.cfalm-los li::before{display:none!important;content:none!important}\n.cfalm-los .ja{display:block;font-weight:bold;color:#172152;line-height:1.6}\n.cfalm-los .en{display:block;font-size:.85em;color:#667;margin-top:.3em;line-height:1.5;word-break:normal!important;overflow-wrap:anywhere}\n.cfalm-sum{background:#f6f7fb;border-radius:6px;padding:1em 1.2em!important;margin:1em 0!important;list-style:none!important}\n.cfalm-sum li{position:relative;margin:.4em 0!important;padding:0 0 0 1.1em!important;line-height:1.7;list-style:none!important}.cfalm-sum li::before{content:\"\"!important;display:block!important;position:absolute!important;left:0!important;top:.7em!important;width:6px!important;height:6px!important;border-radius:50%!important;background:#172152!important;border:none!important;transform:none!important}\n.cfalm-f{background:#f6f7fb;border-left:4px solid #172152;padding:.7em 1em;margin:.8em 0;font-family:\"Menlo\",\"Consolas\",monospace;font-size:.95em;overflow-x:auto}\n.cfalm-nav{background:#f6f7fb;padding:1em 1.2em;border-radius:6px;margin:1em 0;word-break:normal;overflow-wrap:anywhere}\n<\/style>\n<div class=\"box05\">\n<p>Learning Module 5\u300cTime-Series Analysis\uff08\u6642\u7cfb\u5217\u5206\u6790\uff09\u300d\u306f\u3001\u7dda\u5f62\u30fb\u5bfe\u6570\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9\u30fb\u30e2\u30c7\u30eb\u3001\u5171\u5206\u6563\u5b9a\u5e38\u6027\u3068\u81ea\u5df1\u56de\u5e30\uff08AR\uff09\u30e2\u30c7\u30eb\u3001\u5e73\u5747\u56de\u5e30\u3068\u4e88\u6e2c\u7cbe\u5ea6\u306e\u6bd4\u8f03\u3001\u30e9\u30f3\u30c0\u30e0\u30fb\u30a6\u30a9\u30fc\u30af\u3068\u5358\u4f4d\u6839\u3001\u5b63\u7bc0\u6027\u3001ARCH\u3001\u305d\u3057\u3066\u8907\u6570\u306e\u6642\u7cfb\u5217\u3092\u4f7f\u3046\u56de\u5e30\u3067\u306e\u6ce8\u610f\u70b9\u3092\u6271\u3046\u5358\u5143\u3067\u3059\u3002<\/p>\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u3001\u6700\u65b0\u7248\u30ab\u30ea\u30ad\u30e5\u30e9\u30e0\u306eLOS\uff08Learning Outcome Statement\uff09\u3068\u3001\u3053\u306e\u5358\u5143\u306e\u91cd\u8981\u8ad6\u70b9\u3092\u65e5\u672c\u8a9e\u3067\u6574\u7406\u3057\u307e\u3057\u305f\u3002<\/p>\n<\/div>\n<h2>LM5\u306eLOS\uff08\u5b66\u7fd2\u76ee\u6a19\uff09<\/h2>\n<p>LOS\u306f\u3001\u3053\u306e\u5358\u5143\u3067\u300c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3079\u304d\u3053\u3068\u300d\u3068\u3057\u3066\u793a\u3055\u308c\u3066\u3044\u308b\u5b66\u7fd2\u76ee\u6a19\u3067\u3059\u3002LM5\u306b\u306f15\u500b\u306eLOS\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ol class=\"cfalm-los\">\n<li><span class=\"ja\">LOS 1\uff1a\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9\u307e\u305f\u306f\u5bfe\u6570\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9\u3068\u3057\u3066\u30e2\u30c7\u30eb\u5316\u3055\u308c\u305f\u6642\u7cfb\u5217\u306b\u3064\u3044\u3066\u3001\u63a8\u5b9a\u3055\u308c\u305f\u30c8\u30ec\u30f3\u30c9\u4fc2\u6570\u304b\u3089\u4e88\u6e2c\u30c8\u30ec\u30f3\u30c9\u5024\u3092\u8a08\u7b97\u30fb\u8a55\u4fa1\u3059\u308b<\/span><span class=\"en\">calculate and evaluate the predicted trend value for a time series, modeled as either a linear trend or a log-linear trend, given the estimated trend coefficients<\/span><\/li>\n<li><span class=\"ja\">LOS 2\uff1a\u7279\u5b9a\u306e\u6642\u7cfb\u5217\u306b\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9\u3068\u5bfe\u6570\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9\u306e\u3069\u3061\u3089\u3092\u4f7f\u3046\u3079\u304d\u304b\u3092\u6c7a\u3081\u308b\u8981\u56e0\u3092\u8aac\u660e\u3057\u3001\u30c8\u30ec\u30f3\u30c9\u30fb\u30e2\u30c7\u30eb\u306e\u9650\u754c\u3092\u8a55\u4fa1\u3059\u308b<\/span><span class=\"en\">describe factors that determine whether a linear or a log-linear trend should be used with a particular time series and evaluate limitations of trend models<\/span><\/li>\n<li><span class=\"ja\">LOS 3\uff1a\u6642\u7cfb\u5217\u304c\u5171\u5206\u6563\u5b9a\u5e38\u3067\u3042\u308b\u3053\u3068\u306e\u5fc5\u8981\u6027\u3092\u8aac\u660e\u3057\u3001\u5b9a\u5e38\u3067\u306a\u3044\u6642\u7cfb\u5217\u306e\u610f\u5473\u3092\u8aac\u660e\u3059\u308b<\/span><span class=\"en\">explain the requirement for a time series to be covariance stationary and describe the significance of a series that is not stationary<\/span><\/li>\n<li><span class=\"ja\">LOS 4\uff1ap \u6b21\u306e\u81ea\u5df1\u56de\u5e30\uff08AR\uff09\u30e2\u30c7\u30eb\u306e\u69cb\u9020\u3092\u8aac\u660e\u3057\u3001\u63a8\u5b9a\u4fc2\u6570\u304b\u30891\u671f\u5148\u30fb2\u671f\u5148\u306e\u4e88\u6e2c\u5024\u3092\u8a08\u7b97\u3059\u308b<\/span><span class=\"en\">describe the structure of an autoregressive (AR) model of order p and calculate one- and two-period-ahead forecasts given the estimated coefficients<\/span><\/li>\n<li><span class=\"ja\">LOS 5\uff1a\u6b8b\u5dee\u306e\u81ea\u5df1\u76f8\u95a2\u3092\u4f7f\u3063\u3066\u81ea\u5df1\u56de\u5e30\u30e2\u30c7\u30eb\u304c\u6642\u7cfb\u5217\u306b\u9069\u5408\u3057\u3066\u3044\u308b\u304b\u3092\u691c\u5b9a\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3059\u308b<\/span><span class=\"en\">explain how autocorrelations of the residuals can be used to test whether the autoregressive model fits the time series<\/span><\/li>\n<li><span class=\"ja\">LOS 6\uff1a\u5e73\u5747\u56de\u5e30\u3092\u8aac\u660e\u3057\u3001\u5e73\u5747\u56de\u5e30\u6c34\u6e96\u3092\u8a08\u7b97\u3059\u308b<\/span><span class=\"en\">explain mean reversion and calculate a mean-reverting level<\/span><\/li>\n<li><span class=\"ja\">LOS 7\uff1a\u30b5\u30f3\u30d7\u30eb\u5185\u4e88\u6e2c\u3068\u30b5\u30f3\u30d7\u30eb\u5916\u4e88\u6e2c\u3092\u5bfe\u6bd4\u3057\u3001\u5e73\u5747\u4e8c\u4e57\u8aa4\u5dee\u306e\u5e73\u65b9\u6839\uff08RMSE\uff09\u306e\u57fa\u6e96\u306b\u57fa\u3065\u3044\u3066\u7570\u306a\u308b\u6642\u7cfb\u5217\u30e2\u30c7\u30eb\u306e\u4e88\u6e2c\u7cbe\u5ea6\u3092\u6bd4\u8f03\u3059\u308b<\/span><span class=\"en\">contrast in-sample and out-of-sample forecasts and compare the forecasting accuracy of different time-series models based on the root mean squared error criterion<\/span><\/li>\n<li><span class=\"ja\">LOS 8\uff1a\u6642\u7cfb\u5217\u30e2\u30c7\u30eb\u306e\u4fc2\u6570\u306e\u4e0d\u5b89\u5b9a\u6027\u3092\u8aac\u660e\u3059\u308b<\/span><span class=\"en\">explain the instability of coefficients of time-series models<\/span><\/li>\n<li><span class=\"ja\">LOS 9\uff1a\u30e9\u30f3\u30c0\u30e0\u30fb\u30a6\u30a9\u30fc\u30af\u904e\u7a0b\u306e\u7279\u5fb4\u3092\u8aac\u660e\u3057\u3001\u5171\u5206\u6563\u5b9a\u5e38\u904e\u7a0b\u3068\u5bfe\u6bd4\u3059\u308b<\/span><span class=\"en\">describe characteristics of random walk processes and contrast them to covariance stationary processes<\/span><\/li>\n<li><span class=\"ja\">LOS 10\uff1a\u5358\u4f4d\u6839\u304c\u6642\u7cfb\u5217\u5206\u6790\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u3092\u8aac\u660e\u3057\u3001\u5358\u4f4d\u6839\u304c\u751f\u3058\u3084\u3059\u3044\u5834\u5408\u3068\u305d\u306e\u691c\u5b9a\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u3001\u5358\u4f4d\u6839\u3092\u3082\u3064\u6642\u7cfb\u5217\u3092 AR \u30e2\u30c7\u30eb\u3067\u5206\u6790\u3067\u304d\u308b\u3088\u3046\u5909\u63db\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3059<\/span><span class=\"en\">describe implications of unit roots for time-series analysis, explain when unit roots are likely to occur and how to test for them, and demonstrate how a time series with a unit root can be transformed so it can be analyzed with an AR model<\/span><\/li>\n<li><span class=\"ja\">LOS 11\uff1a\u975e\u5b9a\u5e38\u6027\u306b\u95a2\u3059\u308b\u5358\u4f4d\u6839\u691c\u5b9a\u306e\u624b\u9806\u3092\u8aac\u660e\u3057\u3001\u305d\u306e\u691c\u5b9a\u3068\u81ea\u5df1\u56de\u5e30\u6642\u7cfb\u5217\u30e2\u30c7\u30eb\u3068\u306e\u95a2\u4fc2\u3092\u8aac\u660e\u3059\u308b<\/span><span class=\"en\">describe the steps of the unit root test for nonstationarity and explain the relation of the test to autoregressive time-series models<\/span><\/li>\n<li><span class=\"ja\">LOS 12\uff1a\u6642\u7cfb\u5217\u30e2\u30c7\u30eb\u306b\u304a\u3051\u308b\u5b63\u7bc0\u6027\u306e\u691c\u5b9a\u3068\u4fee\u6b63\u306e\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u3001\u5b63\u7bc0\u30e9\u30b0\u3092\u542b\u3080 AR \u30e2\u30c7\u30eb\u306b\u3088\u308b\u4e88\u6e2c\u5024\u3092\u8a08\u7b97\u30fb\u89e3\u91c8\u3059\u308b<\/span><span class=\"en\">explain how to test and correct for seasonality in a time-series model and calculate and interpret a forecasted value using an AR model with a seasonal lag<\/span><\/li>\n<li><span class=\"ja\">LOS 13\uff1a\u81ea\u5df1\u56de\u5e30\u6761\u4ef6\u4ed8\u304d\u4e0d\u5747\u4e00\u5206\u6563\uff08ARCH\uff09\u3092\u8aac\u660e\u3057\u3001ARCH \u30e2\u30c7\u30eb\u3092\u6642\u7cfb\u5217\u306e\u5206\u6563\u306e\u4e88\u6e2c\u306b\u5fdc\u7528\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3059\u308b<\/span><span class=\"en\">explain autoregressive conditional heteroskedasticity (ARCH) and describe how ARCH models can be applied to predict the variance of a time series<\/span><\/li>\n<li><span class=\"ja\">LOS 14\uff1a\u7dda\u5f62\u56de\u5e30\u3067\u4f7f\u3046\u524d\u306b\u3001\u6642\u7cfb\u5217\u5909\u6570\u306e\u975e\u5b9a\u5e38\u6027\u3084\u5171\u548c\u5206\u3092\u3069\u306e\u3088\u3046\u306b\u5206\u6790\u3059\u3079\u304d\u304b\u3092\u8aac\u660e\u3059\u308b<\/span><span class=\"en\">explain how time-series variables should be analyzed for nonstationarity and\/or cointegration before use in a linear regression<\/span><\/li>\n<li><span class=\"ja\">LOS 15\uff1a\u4e0e\u3048\u3089\u308c\u305f\u6295\u8cc7\u4e0a\u306e\u554f\u984c\u3092\u5206\u6790\u3059\u308b\u306e\u306b\u9069\u5207\u306a\u6642\u7cfb\u5217\u30e2\u30c7\u30eb\u3092\u5224\u65ad\u3057\u3001\u305d\u306e\u9078\u629e\u3092\u6b63\u5f53\u5316\u3059\u308b<\/span><span class=\"en\">determine an appropriate time-series model to analyze a given investment problem and justify that choice<\/span><\/li>\n<\/ol>\n<h2>LM5\u306e\u307e\u3068\u3081<\/h2>\n<p>\u3053\u306e\u5358\u5143\u306e\u8981\u70b9\u3092\u307e\u3068\u3081\u308b\u3068\u3001\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<ul class=\"cfalm-sum\">\n<li>\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9\u30fb\u30e2\u30c7\u30eb\u306e t \u671f\u306e\u4e88\u6e2c\u5024\u306f b\u03020 + b\u03021t\u3001\u5bfe\u6570\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9\u30fb\u30e2\u30c7\u30eb\u3067\u306f e^(b\u03020 + b\u03021t)<\/li>\n<li>\u4e00\u5b9a\u306e\u984d\u3067\u5897\u3048\u308b\u7cfb\u5217\u306b\u306f\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9\u3001\u4e00\u5b9a\u306e\u7387\u3067\u5897\u3048\u308b\u7cfb\u5217\u306b\u306f\u5bfe\u6570\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9\u304c\u9069\u3059\u308b\u3002\u30c8\u30ec\u30f3\u30c9\u30fb\u30e2\u30c7\u30eb\u306e\u8aa4\u5dee\u306b\u7cfb\u5217\u76f8\u95a2\u304c\u3042\u308c\u3070\u5225\u306e\u30e2\u30c7\u30eb\u304c\u5fc5\u8981<\/li>\n<li>\u5171\u5206\u6563\u5b9a\u5e38\u306e\u6761\u4ef6\u306f\u3001\u671f\u5f85\u5024\u30fb\u5206\u6563\u30fb\u4e00\u5b9a\u30e9\u30b0\u306e\u81ea\u5df1\u5171\u5206\u6563\u304c\u3059\u3079\u3066\u306e\u671f\u9593\u3067\u4e00\u5b9a\u304b\u3064\u6709\u9650\u3067\u3042\u308b\u3053\u3068\u3002\u5b9a\u5e38\u3067\u306a\u3044\u7cfb\u5217\u306b\u7dda\u5f62\u56de\u5e30\u3067 AR \u30e2\u30c7\u30eb\u3092\u63a8\u5b9a\u3057\u3066\u3082\u6709\u52b9\u3067\u306a\u3044<\/li>\n<li>AR \u30e2\u30c7\u30eb\u304c\u9069\u5408\u3057\u3066\u3044\u308c\u3070\u3001\u8aa4\u5dee\u9805\u306e\u81ea\u5df1\u76f8\u95a2\u306f\u3059\u3079\u3066\u306e\u30e9\u30b0\u3067\u30bc\u30ed\u3002\u5171\u5206\u6563\u5b9a\u5e38\u306a\u7cfb\u5217\u306f\u5e73\u5747\u56de\u5e30\u7684\u3067\u3001\u9577\u671f\u5e73\u5747\u3088\u308a\u4e0a\u306a\u3089\u4e0b\u304c\u308a\u3001\u4e0b\u306a\u3089\u4e0a\u304c\u308b<\/li>\n<li>\u4e88\u6e2c\u6027\u80fd\u306e\u8a55\u4fa1\u3067\u306f\u30b5\u30f3\u30d7\u30eb\u5916\u4e88\u6e2c\u304c\u91cd\u8981\u3067\u3001RMSE \u304c\u5c0f\u3055\u3044\u307b\u3069\u4e88\u6e2c\u7cbe\u5ea6\u304c\u9ad8\u3044<\/li>\n<li>\u30e9\u30f3\u30c0\u30e0\u30fb\u30a6\u30a9\u30fc\u30af\u306f\u5358\u4f4d\u6839\u3092\u3082\u3061\u5171\u5206\u6563\u5b9a\u5e38\u3067\u306f\u306a\u3044\u30021\u968e\u306e\u968e\u5dee\u3092\u3068\u308b\u3053\u3068\u3067\u5b9a\u5e38\u7cfb\u5217\u306b\u5909\u63db\u3067\u304d\u308b\u5834\u5408\u304c\u3042\u308b<\/li>\n<li>\u5b63\u7bc0\u30e9\u30b0\u3067\u7cfb\u5217\u76f8\u95a2\u304c\u6709\u610f\u306a\u3089\u5b63\u7bc0\u6027\u304c\u3042\u308a\u3001\u5b63\u7bc0\u30e9\u30b0\u3092\u52a0\u3048\u3066\u30e2\u30c7\u30eb\u5316\u3059\u308b\u3002\u8aa4\u5dee\u306e\u5206\u6563\u304c\u904e\u53bb\u306e\u8aa4\u5dee\u306e\u5206\u6563\u306b\u4f9d\u5b58\u3059\u308b ARCH \u306f\u3001\u6b8b\u5dee2\u4e57\u3092\u305d\u306e1\u671f\u524d\u306e\u5024\u306b\u56de\u5e30\u3057\u3066\u691c\u5b9a\u3059\u308b<\/li>\n<li>2\u3064\u306e\u6642\u7cfb\u5217\u306e\u56de\u5e30\u3067\u306f\u5358\u4f4d\u6839\u306e\u6709\u7121\u3092\u78ba\u8a8d\u3057\u3001\u4e21\u65b9\u306b\u5358\u4f4d\u6839\u304c\u3042\u308b\u5834\u5408\u306f\u5171\u548c\u5206\u3057\u3066\u3044\u308b\u3068\u304d\u306b\u9650\u308a\u56de\u5e30\u304c\u6709\u52b9<\/li>\n<\/ul>\n<p>\u4ee5\u4e0b\u3001LOS\u3054\u3068\u306b\u91cd\u8981\u8ad6\u70b9\u3092\u6574\u7406\u3057\u307e\u3059\u3002<\/p>\n<h3>LOS 1\uff1a\u7dda\u5f62\u30fb\u5bfe\u6570\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9\u306e\u4e88\u6e2c\u5024<\/h3>\n<p>\u30c8\u30ec\u30f3\u30c9\u30fb\u30e2\u30c7\u30eb\u306f\u6642\u9593 t \u3060\u3051\u3092\u72ec\u7acb\u5909\u6570\u3068\u3059\u308b\u56de\u5e30\u3067\u3059\u3002<strong>\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9<\/strong>\u306f\u6bce\u671f\u4e00\u5b9a\u984d\u306e\u5897\u52a0\u3001<strong>\u5bfe\u6570\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9<\/strong>\u306f\u6bce\u671f\u4e00\u5b9a\u7387\u306e\u6210\u9577\u3092\u8868\u3057\u3001\u4e88\u6e2c\u5024\u306f\u63a8\u5b9a\u4fc2\u6570\u306b t \u3092\u4ee3\u5165\u3057\u3066\u6c42\u3081\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u7dda\u5f62\uff1ayt = b0 + b1t + \u03b5t<\/li>\n<li>\u5bfe\u6570\u7dda\u5f62\uff1aln yt = b0 + b1t + \u03b5t<\/li>\n<li>\u5bfe\u6570\u7dda\u5f62\u306e\u4e88\u6e2c\u5024\u306f\u6307\u6570\u3092\u3068\u3063\u3066\u5143\u306e\u6c34\u6e96\u306b\u623b\u3059<\/li>\n<li>t \u306f\u671f\u9593\u756a\u53f7\uff08\u521d\u671f\u30921\u3068\u3059\u308b\u306a\u3069\uff09<\/li>\n<\/ul>\n<div class=\"cfalm-f\">\u7dda\u5f62\uff1a\u0177t = b\u03020 + b\u03021t\u3001\u5bfe\u6570\u7dda\u5f62\uff1a\u0177t = e^(b\u03020 + b\u03021t)<\/div>\n<h3>LOS 2\uff1a\u30c8\u30ec\u30f3\u30c9\u30fb\u30e2\u30c7\u30eb\u306e\u9078\u3073\u65b9\u3068\u9650\u754c<\/h3>\n<p>\u30c7\u30fc\u30bf\u306e\u30d7\u30ed\u30c3\u30c8\u304c\u76f4\u7dda\u7684\u306a\u3089\u7dda\u5f62\u3001\u6307\u6570\u7684\u306b\u4f38\u3073\u308b\uff08\u6210\u9577\u7387\u304c\u4e00\u5b9a\uff09\u306a\u3089\u5bfe\u6570\u7dda\u5f62\u3092\u9078\u3073\u307e\u3059\u3002\u305f\u3060\u3057\u30c8\u30ec\u30f3\u30c9\u30fb\u30e2\u30c7\u30eb\u306f\u8aa4\u5dee\u306b<strong>\u7cfb\u5217\u76f8\u95a2<\/strong>\u304c\u6b8b\u308a\u3084\u3059\u304f\u3001\u305d\u306e\u5834\u5408\u306f\u524d\u63d0\u9055\u53cd\u3068\u306a\u308b\u305f\u3081\u5225\u306e\u30e2\u30c7\u30eb\uff08AR \u30e2\u30c7\u30eb\u306a\u3069\uff09\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u4e00\u5b9a\u984d\u306e\u5897\u52a0 \u2192 \u7dda\u5f62\u30c8\u30ec\u30f3\u30c9<\/li>\n<li>\u4e00\u5b9a\u7387\u306e\u6210\u9577 \u2192 \u5bfe\u6570\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9<\/li>\n<li>\u7cfb\u5217\u76f8\u95a2\u306e\u78ba\u8a8d\uff1a\u30c0\u30fc\u30d3\u30f3\u30fb\u30ef\u30c8\u30bd\u30f3\uff08DW\uff09\u7d71\u8a08\u91cf\u304c2\u304b\u3089\u5927\u304d\u304f\u96e2\u308c\u3066\u3044\u306a\u3044\u304b<\/li>\n<li>\u7cfb\u5217\u76f8\u95a2\u304c\u3042\u308c\u3070\u6a19\u6e96\u8aa4\u5dee\u30fb\u691c\u5b9a\u304c\u4fe1\u983c\u3067\u304d\u306a\u3044<\/li>\n<\/ul>\n<h3>LOS 3\uff1a\u5171\u5206\u6563\u5b9a\u5e38\u6027\u306e\u5fc5\u8981\u6027<\/h3>\n<p>AR \u30e2\u30c7\u30eb\u3092\u7dda\u5f62\u56de\u5e30\u3067\u63a8\u5b9a\u3059\u308b\u306b\u306f\u3001\u6642\u7cfb\u5217\u304c<strong>\u5171\u5206\u6563\u5b9a\u5e38\uff08covariance stationary\uff09<\/strong>\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u5b9a\u5e38\u3067\u306a\u3044\u7cfb\u5217\u306b\u305d\u306e\u307e\u307e\u56de\u5e30\u3092\u4f7f\u3046\u3068\u63a8\u5b9a\u7d50\u679c\u304c\u7121\u610f\u5473\u306b\u306a\u308b\u304a\u305d\u308c\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u6761\u4ef61\uff1a\u671f\u5f85\u5024\u304c\u4e00\u5b9a\u304b\u3064\u6709\u9650<\/li>\n<li>\u6761\u4ef62\uff1a\u5206\u6563\u304c\u4e00\u5b9a\u304b\u3064\u6709\u9650<\/li>\n<li>\u6761\u4ef63\uff1a\u4e00\u5b9a\u30e9\u30b0\u306e\u81ea\u5df1\u5171\u5206\u6563\u304c\u4e00\u5b9a\u304b\u3064\u6709\u9650<\/li>\n<li>\u975e\u5b9a\u5e38\u306e\u5146\u5019\uff1a\u660e\u78ba\u306a\u30c8\u30ec\u30f3\u30c9\uff08\u5e73\u5747\u304c\u5909\u5316\uff09\u3084\u5206\u6563\u306e\u5909\u5316<\/li>\n<\/ul>\n<h3>LOS 4\uff1aAR(p) \u30e2\u30c7\u30eb\u306e\u69cb\u9020\u3068\u591a\u671f\u5148\u4e88\u6e2c<\/h3>\n<p><strong>p \u6b21\u306e\u81ea\u5df1\u56de\u5e30\u30e2\u30c7\u30eb AR(p)<\/strong> \u306f\u3001\u7cfb\u5217\u81ea\u8eab\u306e\u904e\u53bb p \u671f\u306e\u5024\u3067\u73fe\u5728\u306e\u5024\u3092\u8aac\u660e\u3057\u307e\u3059\u30022\u671f\u5148\u306e\u4e88\u6e2c\u306f\u30011\u671f\u5148\u306e\u4e88\u6e2c\u5024\u3092\u518d\u3073\u5f0f\u306b\u4ee3\u5165\u3059\u308b<strong>\u9023\u9396\u5247\uff08chain rule of forecasting\uff09<\/strong>\u3067\u6c42\u3081\u307e\u3059\u3002<\/p>\n<ul>\n<li>AR(1)\uff1axt = b0 + b1xt\u22121 + \u03b5t<\/li>\n<li>1\u671f\u5148\uff1ax\u0302t+1 = b\u03020 + b\u03021xt<\/li>\n<li>2\u671f\u5148\uff1ax\u0302t+2 = b\u03020 + b\u03021x\u0302t+1<\/li>\n<li>\u5148\u306e\u4e88\u6e2c\u307b\u3069\u4e0d\u78ba\u5b9f\u6027\u304c\u5927\u304d\u3044<\/li>\n<\/ul>\n<div class=\"cfalm-f\">xt = b0 + b1xt\u22121 + b2xt\u22122 + \u2026 + bpxt\u2212p + \u03b5t<\/div>\n<h3>LOS 5\uff1a\u6b8b\u5dee\u306e\u81ea\u5df1\u76f8\u95a2\u306b\u3088\u308b\u30e2\u30c7\u30eb\u9069\u5408\u306e\u691c\u5b9a<\/h3>\n<p>AR \u30e2\u30c7\u30eb\u304c\u9069\u5207\u306a\u3089\u3001<strong>\u6b8b\u5dee\u306e\u81ea\u5df1\u76f8\u95a2\u306f\u3059\u3079\u3066\u306e\u30e9\u30b0\u3067\u30bc\u30ed<\/strong>\u306b\u306a\u308b\u306f\u305a\u3067\u3059\u3002\u5404\u30e9\u30b0\u306e\u6b8b\u5dee\u81ea\u5df1\u76f8\u95a2\u3092 t \u691c\u5b9a\u3057\u3001\u6709\u610f\u306a\u3082\u306e\u304c\u3042\u308c\u3070\u30e9\u30b0\u3092\u8ffd\u52a0\u3059\u308b\u306a\u3069\u30e2\u30c7\u30eb\u3092\u898b\u76f4\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u624b\u9806\uff1aAR(1) \u3092\u63a8\u5b9a\u2192\u6b8b\u5dee\u306e\u81ea\u5df1\u76f8\u95a2\u3092\u8a08\u7b97\u2192\u6709\u610f\u6027\u3092\u691c\u5b9a<\/li>\n<li>\u81ea\u5df1\u76f8\u95a2\u306e\u6a19\u6e96\u8aa4\u5dee\u306f 1\/\u221aT\uff08T \u306f\u89b3\u6e2c\u6570\uff09<\/li>\n<li>\u6709\u610f\u306a\u81ea\u5df1\u76f8\u95a2\u304c\u3042\u308c\u3070\u30e2\u30c7\u30eb\u306f\u4e0d\u9069\u5207<\/li>\n<li>AR \u30e2\u30c7\u30eb\u3067\u306f DW \u7d71\u8a08\u91cf\u306f\u4f7f\u3048\u306a\u3044<\/li>\n<\/ul>\n<div class=\"cfalm-f\">t = \u6b8b\u5dee\u306e\u81ea\u5df1\u76f8\u95a2 \u00f7 (1\/\u221aT)<\/div>\n<h3>LOS 6\uff1a\u5e73\u5747\u56de\u5e30\u3068\u5e73\u5747\u56de\u5e30\u6c34\u6e96<\/h3>\n<p><strong>\u5e73\u5747\u56de\u5e30\uff08mean reversion\uff09<\/strong>\u3068\u306f\u3001\u9577\u671f\u5e73\u5747\u3088\u308a\u9ad8\u3051\u308c\u3070\u4e0b\u304c\u308a\u3001\u4f4e\u3051\u308c\u3070\u4e0a\u304c\u308b\u6027\u8cea\u3067\u3059\u3002AR(1) \u3067\u306f |b1| < 1 \u306e\u3068\u304d\u6709\u9650\u306e\u5e73\u5747\u56de\u5e30\u6c34\u6e96\u3092\u3082\u3061\u3001\u73fe\u5728\u5024\u304c\u305d\u306e\u6c34\u6e96\u306b\u3042\u308c\u3070\u6b21\u671f\u306e\u4e88\u6e2c\u5024\u3082\u540c\u3058\u306b\u306a\u308a\u307e\u3059\u3002\n\n\n\n<ul>\n<li>\u5171\u5206\u6563\u5b9a\u5e38\u306a\u7cfb\u5217\u306f\u5e73\u5747\u56de\u5e30\u7684<\/li>\n<li>|b1| < 1 \u304c\u6761\u4ef6\uff08b1 = 1 \u306f\u5358\u4f4d\u6839\uff09<\/li>\n<li>\u73fe\u5728\u5024\u304c\u5e73\u5747\u56de\u5e30\u6c34\u6e96\u3088\u308a\u4e0a\u306a\u3089\u4e88\u6e2c\u5024\u306f\u4e0b\u304c\u308b<\/li>\n<\/ul>\n<div class=\"cfalm-f\">\u5e73\u5747\u56de\u5e30\u6c34\u6e96 = b0 \/ (1 \u2212 b1)<\/div>\n<h3>LOS 7\uff1a\u30b5\u30f3\u30d7\u30eb\u5185\u30fb\u30b5\u30f3\u30d7\u30eb\u5916\u4e88\u6e2c\u3068 RMSE<\/h3>\n<p><strong>\u30b5\u30f3\u30d7\u30eb\u5185\u4e88\u6e2c<\/strong>\u306f\u63a8\u5b9a\u306b\u4f7f\u3063\u305f\u671f\u9593\u306e\u5f53\u3066\u306f\u307e\u308a\u3001<strong>\u30b5\u30f3\u30d7\u30eb\u5916\u4e88\u6e2c<\/strong>\u306f\u63a8\u5b9a\u671f\u9593\u5916\u3067\u306e\u4e88\u6e2c\u3067\u3001\u5b9f\u52d9\u4e0a\u306f\u30b5\u30f3\u30d7\u30eb\u5916\u306e\u7cbe\u5ea6\u304c\u3088\u308a\u91cd\u8981\u3067\u3059\u3002\u30e2\u30c7\u30eb\u9593\u306e\u6bd4\u8f03\u306b\u306f<strong>RMSE\uff08\u5e73\u5747\u4e8c\u4e57\u8aa4\u5dee\u306e\u5e73\u65b9\u6839\uff09<\/strong>\u3092\u4f7f\u3044\u3001\u5c0f\u3055\u3044\u307b\u3069\u7cbe\u5ea6\u304c\u9ad8\u3044\u3068\u5224\u65ad\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u30b5\u30f3\u30d7\u30eb\u5916\u4e88\u6e2c\u306f\u5c06\u6765\u30c7\u30fc\u30bf\u3078\u306e\u6c4e\u5316\u529b\u3092\u793a\u3059<\/li>\n<li>RMSE\uff1a\u4e88\u6e2c\u8aa4\u5dee\u306e2\u4e57\u306e\u5e73\u5747\u306e\u5e73\u65b9\u6839<\/li>\n<li>RMSE \u304c\u6700\u5c0f\u306e\u30e2\u30c7\u30eb\u3092\u9078\u3076<\/li>\n<li>\u30b5\u30f3\u30d7\u30eb\u5185\u3067\u512a\u308c\u3066\u3044\u3066\u3082\u30b5\u30f3\u30d7\u30eb\u5916\u3067\u52a3\u308b\u3053\u3068\u304c\u3042\u308b<\/li>\n<\/ul>\n<div class=\"cfalm-f\">RMSE = \u221a[\u03a3(\u5b9f\u7e3e\u5024 \u2212 \u4e88\u6e2c\u5024)\u00b2 \/ n]<\/div>\n<h3>LOS 8\uff1a\u6642\u7cfb\u5217\u30e2\u30c7\u30eb\u306e\u4fc2\u6570\u306e\u4e0d\u5b89\u5b9a\u6027<\/h3>\n<p>\u6642\u7cfb\u5217\u30e2\u30c7\u30eb\u306e\u4fc2\u6570\u306f\u3001\u63a8\u5b9a\u671f\u9593\u306b\u3088\u3063\u3066\u5927\u304d\u304f\u5909\u308f\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u7d4c\u6e08\u74b0\u5883\u3084\u898f\u5236\u306e\u5909\u5316\u3067\u7cfb\u5217\u306e\u6027\u8cea\u304c\u5909\u308f\u308b\u305f\u3081\u3067\u3001<strong>\u63a8\u5b9a\u671f\u9593\u4e2d\u306b\u7cfb\u5217\u304c\u5b9a\u5e38\u3067\u3042\u3063\u305f<\/strong>\u3053\u3068\u3092\u78ba\u8a8d\u3057\u3066\u671f\u9593\u3092\u9078\u3076\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u671f\u9593\u306e\u9577\u3055\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\uff1a\u9577\u3044\u307b\u3069\u7d71\u8a08\u7684\u4fe1\u983c\u6027\u2191\u3001\u69cb\u9020\u5909\u5316\u306e\u6df7\u5165\u30ea\u30b9\u30af\u2191<\/li>\n<li>\u69cb\u9020\u5909\u5316\u306e\u524d\u5f8c\u306f\u5206\u3051\u3066\u63a8\u5b9a\u3092\u691c\u8a0e<\/li>\n<li>\u5b9a\u5e38\u6027\u306e\u78ba\u8a8d\u304c\u671f\u9593\u9078\u629e\u306e\u524d\u63d0<\/li>\n<li>\u4fc2\u6570\u306e\u5b89\u5b9a\u6027\u306f\u30e2\u30c7\u30eb\u306e\u4fe1\u983c\u6027\u3092\u5de6\u53f3<\/li>\n<\/ul>\n<h3>LOS 9\uff1a\u30e9\u30f3\u30c0\u30e0\u30fb\u30a6\u30a9\u30fc\u30af\u3068\u5171\u5206\u6563\u5b9a\u5e38\u904e\u7a0b<\/h3>\n<p><strong>\u30e9\u30f3\u30c0\u30e0\u30fb\u30a6\u30a9\u30fc\u30af<\/strong>\u306f\u3001\u4eca\u671f\u306e\u5024\u304c\u524d\u671f\u306e\u5024\u306b\u4e88\u6e2c\u4e0d\u80fd\u306a\u8aa4\u5dee\u3092\u52a0\u3048\u305f\u3082\u306e\u306b\u306a\u308b\u7cfb\u5217\u3067\u3001AR(1) \u3067 b0 = 0\u3001b1 = 1 \u306e\u5834\u5408\u306b\u3042\u305f\u308a\u307e\u3059\u3002\u5e73\u5747\u56de\u5e30\u6c34\u6e96\u304c\u5b9a\u7fa9\u3067\u304d\u305a\u5206\u6563\u3082\u6642\u9593\u3068\u3068\u3082\u306b\u5897\u5927\u3059\u308b\u305f\u3081\u3001<strong>\u5171\u5206\u6563\u5b9a\u5e38\u3067\u306f\u3042\u308a\u307e\u305b\u3093<\/strong>\u3002<\/p>\n<ul>\n<li>\u30e9\u30f3\u30c0\u30e0\u30fb\u30a6\u30a9\u30fc\u30af\uff1axt = xt\u22121 + \u03b5t<\/li>\n<li>\u30c9\u30ea\u30d5\u30c8\u4ed8\u304d\uff1axt = b0 + xt\u22121 + \u03b5t\uff08b0 \u2260 0\uff09<\/li>\n<li>\u3059\u3079\u3066\u306e\u30e9\u30f3\u30c0\u30e0\u30fb\u30a6\u30a9\u30fc\u30af\u306f\u5358\u4f4d\u6839\u3092\u3082\u3064<\/li>\n<li>\u5e73\u5747\u56de\u5e30\u6c34\u6e96 b0\/(1\u2212b1) \u306f\u5206\u6bcd\u30bc\u30ed\u3067\u5b9a\u7fa9\u3067\u304d\u306a\u3044<\/li>\n<li>\u8aa4\u5dee\u306e\u5206\u6563\u304c\u6642\u9593\u3068\u3068\u3082\u306b\u62e1\u5927<\/li>\n<\/ul>\n<h3>LOS 10\uff1a\u5358\u4f4d\u6839\u306e\u5f71\u97ff\u3068\u968e\u5dee\u5909\u63db<\/h3>\n<p>\u7cfb\u5217\u304c<strong>\u5358\u4f4d\u6839\uff08b1 = 1\uff09<\/strong>\u3092\u3082\u3064\u3068\u5171\u5206\u6563\u5b9a\u5e38\u3067\u306a\u304f\u306a\u308a\u3001\u901a\u5e38\u306e\u56de\u5e30\u306b\u3088\u308b\u63a8\u5b9a\u3084 t \u691c\u5b9a\u304c\u4fe1\u983c\u3067\u304d\u307e\u305b\u3093\u3002\u5358\u4f4d\u6839\u306f\u8cc7\u7523\u4fa1\u683c\u3084\u70ba\u66ff\u30ec\u30fc\u30c8\u306a\u3069\u3067\u751f\u3058\u3084\u3059\u304f\u3001<strong>1\u968e\u306e\u968e\u5dee\uff08yt = xt \u2212 xt\u22121\uff09<\/strong>\u3092\u3068\u308c\u3070\u5b9a\u5e38\u306b\u306a\u308a AR \u30e2\u30c7\u30eb\u3067\u5206\u6790\u3067\u304d\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u5358\u4f4d\u6839\u304c\u3042\u308b\u3068 AR \u4fc2\u6570\u306e t \u691c\u5b9a\u306f\u7121\u52b9<\/li>\n<li>\u5358\u4f4d\u6839\u306f\u81ea\u5df1\u76f8\u95a2\u306e\u691c\u5b9a\u3067\u306f\u306a\u304f Dickey\u2013Fuller \u691c\u5b9a\u3067\u8abf\u3079\u308b<\/li>\n<li>\u968e\u5dee\u3092\u3068\u3063\u305f\u30e9\u30f3\u30c0\u30e0\u30fb\u30a6\u30a9\u30fc\u30af\u306f\u5e73\u5747\u30bc\u30ed\u30fb\u5206\u6563\u4e00\u5b9a\u306e\u5b9a\u5e38\u7cfb\u5217<\/li>\n<li>\u968e\u5dee\u7cfb\u5217 yt \u306b AR \u30e2\u30c7\u30eb\u3092\u5f53\u3066\u306f\u3081\u308b<\/li>\n<\/ul>\n<div class=\"cfalm-f\">yt = xt \u2212 xt\u22121 = \u03b5t<\/div>\n<h3>LOS 11\uff1a\u5358\u4f4d\u6839\u691c\u5b9a\uff08Dickey\u2013Fuller\uff09\u306e\u624b\u9806<\/h3>\n<p><strong>Dickey\u2013Fuller \u691c\u5b9a<\/strong>\u306f\u3001AR(1) \u306e\u4e21\u8fba\u304b\u3089 xt\u22121 \u3092\u5f15\u3044\u305f\u5f0f\u3067 g1 = b1 \u2212 1 \u304c\u30bc\u30ed\u304b\u3092\u691c\u5b9a\u3057\u307e\u3059\u3002\u5e30\u7121\u4eee\u8aac\u306f\u300c\u5358\u4f4d\u6839\u3042\u308a\uff08g1 = 0\uff09\u300d\u3067\u3001\u901a\u5e38\u306e t \u5206\u5e03\u3067\u306f\u306a\u304f\u5c02\u7528\u306e\u4fee\u6b63\u81e8\u754c\u5024\u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u5909\u5f62\u5f0f\uff1axt \u2212 xt\u22121 = b0 + g1xt\u22121 + \u03b5t<\/li>\n<li>H0\uff1ag1 = 0\uff08\u5358\u4f4d\u6839\u3042\u308a\u30fb\u975e\u5b9a\u5e38\uff09<\/li>\n<li>H1\uff1ag1 < 0\uff08\u5b9a\u5e38\uff09<\/li>\n<li>\u4fee\u6b63\u3055\u308c\u305f\u81e8\u754c\u5024\uff08\u901a\u5e38\u3088\u308a\u7d76\u5bfe\u5024\u304c\u5927\u304d\u3044\uff09\u3092\u4f7f\u7528<\/li>\n<li>\u68c4\u5374\u3067\u304d\u306a\u3051\u308c\u3070\u968e\u5dee\u3092\u3068\u3063\u3066\u5206\u6790<\/li>\n<\/ul>\n<div class=\"cfalm-f\">xt \u2212 xt\u22121 = b0 + (b1 \u2212 1)xt\u22121 + \u03b5t<\/div>\n<h3>LOS 12\uff1a\u5b63\u7bc0\u6027\u306e\u691c\u5b9a\u30fb\u4fee\u6b63\u3068\u5b63\u7bc0\u30e9\u30b0\u4ed8\u304d\u4e88\u6e2c<\/h3>\n<p>\u6b8b\u5dee\u306e\u81ea\u5df1\u76f8\u95a2\u304c<strong>\u5b63\u7bc0\u30e9\u30b0<\/strong>\uff08\u56db\u534a\u671f\u30c7\u30fc\u30bf\u306a\u30894\u671f\u3001\u6708\u6b21\u306a\u308912\u671f\uff09\u3067\u6709\u610f\u306a\u3089\u5b63\u7bc0\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u5b63\u7bc0\u30e9\u30b0\u306e\u9805\u3092\u30e2\u30c7\u30eb\u306b\u52a0\u3048\u3066\u4fee\u6b63\u3057\u3001\u305d\u306e\u5f0f\u306b\u76f4\u8fd1\u5024\u30681\u5e74\u524d\u306e\u5024\u3092\u4ee3\u5165\u3057\u3066\u4e88\u6e2c\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u691c\u51fa\uff1a\u5b63\u7bc0\u30e9\u30b0\u3067\u306e\u6b8b\u5dee\u81ea\u5df1\u76f8\u95a2\u306e t \u691c\u5b9a<\/li>\n<li>\u4fee\u6b63\uff1a\u5b63\u7bc0\u30e9\u30b0\u9805\u3092 AR \u30e2\u30c7\u30eb\u306b\u8ffd\u52a0<\/li>\n<li>\u8ffd\u52a0\u5f8c\u306b\u5b63\u7bc0\u30e9\u30b0\u306e\u81ea\u5df1\u76f8\u95a2\u304c\u6709\u610f\u3067\u306a\u304f\u306a\u308c\u3070\u4fee\u6b63\u6210\u529f<\/li>\n<li>\u56db\u534a\u671f\u30c7\u30fc\u30bf\u306e AR(1) \uff0b\u5b63\u7bc0\u30e9\u30b0\uff1axt = b0 + b1xt\u22121 + b2xt\u22124 + \u03b5t<\/li>\n<\/ul>\n<div class=\"cfalm-f\">x\u0302t+1 = b\u03020 + b\u03021xt + b\u03022xt\u22123\uff08\u56db\u534a\u671f\u30c7\u30fc\u30bf\uff09<\/div>\n<h3>LOS 13\uff1aARCH \u3068\u5206\u6563\u306e\u4e88\u6e2c<\/h3>\n<p><strong>ARCH\uff08\u81ea\u5df1\u56de\u5e30\u6761\u4ef6\u4ed8\u304d\u4e0d\u5747\u4e00\u5206\u6563\uff09<\/strong>\u306f\u3001\u8aa4\u5dee\u306e\u5206\u6563\u304c\u904e\u53bb\u306e\u8aa4\u5dee\u306e\u5927\u304d\u3055\u306b\u4f9d\u5b58\u3059\u308b\u72b6\u614b\u3067\u3059\u3002ARCH \u304c\u3042\u308b\u3068\u4fc2\u6570\u306e\u6a19\u6e96\u8aa4\u5dee\u304c\u8aa4\u308b\u305f\u3081\u4fee\u6b63\u304c\u5fc5\u8981\u3067\u3001\u4e00\u65b9\u3067\u30e2\u30c7\u30eb\u3092\u4f7f\u3063\u3066<strong>\u7fcc\u671f\u306e\u8aa4\u5dee\u5206\u6563\u3092\u4e88\u6e2c<\/strong>\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u691c\u5b9a\uff1a\u6b8b\u5dee2\u4e57\u3092\u305d\u306e1\u671f\u524d\u306e\u6b8b\u5dee2\u4e57\u306b\u56de\u5e30<\/li>\n<li>a1 \u304c\u6709\u610f\u306a\u3089 ARCH(1) \u8aa4\u5dee\u3042\u308a<\/li>\n<li>ARCH \u304c\u3042\u308c\u3070\u4e00\u822c\u5316\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306a\u3069\u3067\u4fee\u6b63<\/li>\n<li>\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u4e88\u6e2c\u306b\u5fdc\u7528<\/li>\n<\/ul>\n<div class=\"cfalm-f\">\u03c3\u0302\u00b2t+1 = \u00e20 + \u00e21\u03b5\u0302\u00b2t<\/div>\n<h3>LOS 14\uff1a\u8907\u6570\u306e\u6642\u7cfb\u5217\u3092\u4f7f\u3046\u56de\u5e30\uff1a\u975e\u5b9a\u5e38\u6027\u3068\u5171\u548c\u5206<\/h3>\n<p>2\u3064\u306e\u6642\u7cfb\u5217\u3067\u56de\u5e30\u3059\u308b\u524d\u306b\u3001\u305d\u308c\u305e\u308c\u306e<strong>\u5358\u4f4d\u6839\u306e\u6709\u7121<\/strong>\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002\u4e21\u65b9\u306b\u5358\u4f4d\u6839\u304c\u3042\u308b\u5834\u5408\u306f\u3001\u9577\u671f\u7684\u306b\u5b89\u5b9a\u3057\u305f\u95a2\u4fc2\u3067\u3042\u308b<strong>\u5171\u548c\u5206\uff08cointegration\uff09<\/strong>\u304c\u3042\u308b\u3068\u304d\u3060\u3051\u56de\u5e30\u304c\u6709\u52b9\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u3069\u3061\u3089\u3082\u5358\u4f4d\u6839\u306a\u3057 \u2192 \u56de\u5e30\u3057\u3066\u3088\u3044<\/li>\n<li>\u4e00\u65b9\u3060\u3051\u5358\u4f4d\u6839\u3042\u308a \u2192 \u56de\u5e30\u306f\u7121\u52b9<\/li>\n<li>\u4e21\u65b9\u5358\u4f4d\u6839\u3042\u308a\u30fb\u5171\u548c\u5206\u306a\u3057 \u2192 \u56de\u5e30\u306f\u7121\u52b9\uff08\u898b\u305b\u304b\u3051\u306e\u56de\u5e30\uff09<\/li>\n<li>\u4e21\u65b9\u5358\u4f4d\u6839\u3042\u308a\u30fb\u5171\u548c\u5206\u3042\u308a \u2192 \u56de\u5e30\u306f\u6709\u52b9<\/li>\n<li>\u5171\u548c\u5206\u306e\u691c\u5b9a\uff1aEngle\u2013Granger \u306e Dickey\u2013Fuller \u691c\u5b9a<\/li>\n<\/ul>\n<h3>LOS 15\uff1a\u6295\u8cc7\u4e0a\u306e\u554f\u984c\u306b\u9069\u3057\u305f\u6642\u7cfb\u5217\u30e2\u30c7\u30eb\u306e\u9078\u629e<\/h3>\n<p>\u30e2\u30c7\u30eb\u9078\u629e\u306f\u3001\u30c7\u30fc\u30bf\u306e\u30d7\u30ed\u30c3\u30c8\u304b\u3089\u30c8\u30ec\u30f3\u30c9\u3084\u5b63\u7bc0\u6027\u3092\u628a\u63e1\u3057\u3001\u5b9a\u5e38\u6027\u3092\u78ba\u8a8d\u3057\u306a\u304c\u3089\u6bb5\u968e\u7684\u306b\u9032\u3081\u307e\u3059\u3002<strong>\u7cfb\u5217\u76f8\u95a2\u30fb\u5358\u4f4d\u6839\u30fb\u5b63\u7bc0\u6027\u30fbARCH<\/strong>\u306e\u78ba\u8a8d\u3092\u9806\u306b\u884c\u3044\u3001\u554f\u984c\u304c\u3042\u308c\u3070\u4fee\u6b63\u3059\u308b\u3053\u3068\u304c\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u76ee\u7684\uff08\u4e88\u6e2c\u30fb\u95a2\u4fc2\u306e\u8aac\u660e\uff09\u3092\u660e\u78ba\u5316<\/li>\n<li>\u30d7\u30ed\u30c3\u30c8\u3067\u30c8\u30ec\u30f3\u30c9\u306e\u6709\u7121\u3068\u5f62\uff08\u7dda\u5f62\u30fb\u6307\u6570\uff09\u3092\u78ba\u8a8d<\/li>\n<li>\u30c8\u30ec\u30f3\u30c9\u30fb\u30e2\u30c7\u30eb\u306e\u6b8b\u5dee\u306b\u7cfb\u5217\u76f8\u95a2\u304c\u3042\u308c\u3070 AR \u30e2\u30c7\u30eb\u3078<\/li>\n<li>\u5358\u4f4d\u6839\u304c\u3042\u308c\u3070\u968e\u5dee\u3092\u3068\u308b\u3001\u5b63\u7bc0\u6027\u304c\u3042\u308c\u3070\u5b63\u7bc0\u30e9\u30b0\u3092\u8ffd\u52a0<\/li>\n<li>ARCH \u3092\u691c\u5b9a\u3057\u3001\u5fc5\u8981\u306a\u3089\u4fee\u6b63<\/li>\n<li>\u8907\u6570\u7cfb\u5217\u306a\u3089\u5358\u4f4d\u6839\u3068\u5171\u548c\u5206\u3092\u78ba\u8a8d<\/li>\n<\/ul>\n<h2>\u52b9\u7387\u3088\u304f\u5b66\u3076\u306b\u306f FA-Academy<\/h2>\n<p>CFA\u00ae\ufe0e\u306e\u5354\u4f1a\u30c6\u30ad\u30b9\u30c8\u306f\u82f1\u8a9e\u3067\u5206\u91cf\u3082\u591a\u304f\u30011\u3064\u3072\u3068\u3064\u306e\u5358\u5143\u3092\u82f1\u8a9e\u3060\u3051\u3067\u7406\u89e3\u3057\u3066\u3044\u304f\u306e\u306f\u5927\u304d\u306a\u8ca0\u62c5\u3067\u3059\u3002<\/p>\n<p>FA-Academy\uff08Financial Analyst Academy\uff09\u306f\u3001<strong>\u65e5\u672c\u8a9e\u3067\u5b66\u3079\u308b\u6570\u5c11\u306a\u3044CFA\u00ae\ufe0e\u8a66\u9a13\u30b5\u30dd\u30fc\u30c8<\/strong>\u3067\u3059\u3002\u3053\u308c\u307e\u3067 Level 1 \u304b\u3089 Level 3 \u307e\u3067\u591a\u304f\u306e\u5408\u683c\u8005\u3092\u8f29\u51fa\u3057\u3066\u304a\u308a\u3001\u5408\u683c\u8005\u306e\u65b9\u3005\u3068\u306e\u5bfe\u8ac7\u3082\u6570\u591a\u304f\u516c\u958b\u3057\u3066\u3044\u307e\u3059\u3002\u3069\u3093\u306a\u65b9\u304c\u3001\u3069\u306e\u3088\u3046\u306b\u5408\u683c\u3055\u308c\u305f\u306e\u304b\u306f<a href=\"https:\/\/triumphmind.com\/cfa\/category\/gokaku\/\" target=\"_blank\" rel=\"noopener\">\u5408\u683c\u8005\u5bfe\u8ac7\u30fb\u5408\u683c\u4f53\u9a13\u8ac7\u306e\u4e00\u89a7<\/a>\u304b\u3089\u3054\u89a7\u3044\u305f\u3060\u3051\u307e\u3059\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/triumphmind.com\/cfa\/level2movie\/\" target=\"_blank\" rel=\"noopener\">Level 2 \u65e5\u672c\u8a9e\u8981\u70b9\u96c6\u306e\u7121\u6599\u30b5\u30f3\u30d7\u30eb\u3092\u53d7\u3051\u53d6\u308b\uff087\u65e5\u9593\u30e1\u30fc\u30eb\u8b1b\u5ea7\uff09<\/a><\/li>\n<li><a href=\"https:\/\/timerex.net\/s\/cfa.tips.slack_2a23\/e72e883e\/\" target=\"_blank\" rel=\"noopener\">\u7121\u6599\u500b\u5225\u9762\u8ac7\u3092\u4e88\u7d04\u3059\u308b\uff08\u5b66\u7fd2\u8a08\u753b\u306e\u3054\u76f8\u8ac7\uff09<\/a><\/li>\n<li><a href=\"https:\/\/triumphmind.com\/cfa\/course\/\" target=\"_blank\" rel=\"noopener\">\u53d7\u8b1b\u6848\u5185\uff08\u30b3\u30fc\u30b9\u4e00\u89a7\u30fb\u53d7\u8b1b\u6599\uff09\u3092\u898b\u308b<\/a><\/li>\n<\/ul>\n<div class=\"cfalm-nav\">\u524d\u306e\u5358\u5143\uff1a<a href=\"https:\/\/triumphmind.com\/cfa\/2026\/09\/22\/cfa-l2-quants-lm4\/\">LM4 Extensions of Multiple Regression\uff08\u91cd\u56de\u5e30\u306e\u62e1\u5f35\uff09<\/a><br \/>\n\u6b21\u306e\u5358\u5143\uff1a<a href=\"https:\/\/triumphmind.com\/cfa\/2026\/09\/22\/cfa-l2-quants-lm6\/\">LM6 Machine Learning\uff08\u6a5f\u68b0\u5b66\u7fd2\uff09<\/a><br \/>\n\u5168\u4f53\u306e\u76ee\u6b21\uff1a<a href=\"https:\/\/triumphmind.com\/cfa\/cfa-curriculum\/#l2-quants\">CFA\u00ae\ufe0e \u5b66\u7fd2\u5185\u5bb9\u306e\u76ee\u6b21\uff08Level 2 Quantitative Methods\uff09<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>CFA\u00ae\ufe0e Level 2 Quantitative Methods LM5\u300cTime-Series Analysis\uff08\u6642\u7cfb\u5217\u5206\u6790\uff09\u300d\u306eLOS\uff08\u5b66\u7fd2\u76ee\u6a19\uff09\u3068\u91cd\u8981\u8ad6\u70b9\u3092\u3001\u6700\u65b0\u7248\u30ab\u30ea\u30ad\u30e5\u30e9\u30e0\u306b\u57fa\u3065\u3044\u3066\u65e5\u672c\u8a9e\u3067\u6574\u7406\u3057\u307e\u3057\u305f\u3002<\/p>\n","protected":false},"author":1,"featured_media":11168,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jin_ogp_image_url":"","_jin_last_featured_id":0,"footnotes":""},"categories":[99],"tags":[],"class_list":["post-10822","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-level2-topics"],"_links":{"self":[{"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/posts\/10822","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/comments?post=10822"}],"version-history":[{"count":1,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/posts\/10822\/revisions"}],"predecessor-version":[{"id":10995,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/posts\/10822\/revisions\/10995"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/media\/11168"}],"wp:attachment":[{"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/media?parent=10822"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/categories?post=10822"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/tags?post=10822"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}