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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Johansen test ： ウィキペディア英語版 Johansen test In statistics, the Johansen test, named after Søren Johansen, is a procedure for testing cointegration of several, say k, I(1) time series. This test permits more than one cointegrating relationship so is more generally applicable than the Engle–Granger test which is based on the Dickey–Fuller (or the augmented) test for unit roots in the residuals from a single (estimated) cointegrating relationship. There are two types of Johansen test, either with trace or with eigenvalue, and the inferences might be a little bit different. The null hypothesis for the trace test is that the number of cointegration vectors is r=r **=1,2,etc. and the first non-rejection of the null is taken as an estimate of r. The null hypothesis for the "maximum eigenvalue" test is as for the trace test but the alternative is r=r *+1 and, again, testing proceeds sequentially for r *=1,2,etc., with the first non-rejection used as an estimator for r. Just like a unit root test, there can be a constant term, a trend term, both, or neither in the model. For a general VAR(''p'') model: :$X\_=\backslash mu+\backslash Phi\; D\_+\backslash Pi\_X\_+\backslash cdots+\backslash Pi\_X\_+e\_,\backslash quad\; t=1,\backslash dots,T$ There are two possible specifications for error correction: that is, two VECM (vector error correction models): 1. The longrun VECM: ::$\backslash Delta\; X\_t\; =\backslash mu+\backslash Phi\; D\_+\backslash Pi\; X\_+\backslash Gamma\_\backslash Delta\; X\_+\backslash cdots+\backslash Gamma\_\backslash Delta\; X\_+\backslash varepsilon\_t,\backslash quad\; t=1,\backslash dots,T$ :where ::$\backslash Gamma\_i\; =\; \backslash Pi\_1\; +\; \backslash cdots\; +\; \backslash Pi\_i\; -\; I,\backslash quad\; i=1,\backslash dots,p-1.\; \backslash ,$ 2. The transitory VECM: ::$\backslash Delta\; X\_=\backslash mu+\backslash Phi\; D\_-\backslash Gamma\_\backslash Delta\; X\_-\backslash cdots-\backslash Gamma\_\backslash Delta\; X\_+\backslash Pi\; X\_+\backslash varepsilon\_,\backslash quad\; t=1,\backslash cdots,T$ :where ::$\backslash Gamma\_i\; =\; \backslash left(\backslash Pi\_+\backslash cdots+\backslash Pi\_p\backslash right),\backslash quad\; i=1,\backslash dots,p-1.\; \backslash ,$ Be aware that the two are the same. In both VECM (Vector Error Correction Model), : $\backslash Pi=\backslash Pi\_+\backslash cdots+\backslash Pi\_-I.\; \backslash ,$ Inferences are drawn on Π, and they will be the same, so is the explanatory power. == References == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Johansen test」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.