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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 Dickey–Fuller test ： ウィキペディア英語版 Dickey–Fuller test In statistics, the Dickey–Fuller test tests whether a unit root is present in an autoregressive model. It is named after the statisticians David Dickey and Wayne Fuller, who developed the test in 1979.〔 --> | url = | format = | accessdate = }}〕 ==Explanation== A simple AR(1) model is : $y\_=\backslash rho\; y\_+u\_\backslash ,$ where $y\_$ is the variable of interest, $t$ is the time index, $\backslash rho$ is a coefficient, and $u\_$ is the error term. A unit root is present if $\backslash rho\; =\; 1$. The model would be non-stationary in this case. The regression model can be written as : $\backslash nabla\; y\_=(\backslash rho-1)y\_+u\_=\backslash delta\; y\_+\; u\_\backslash ,$ where $\backslash nabla$ is the first difference operator. This model can be estimated and testing for a unit root is equivalent to testing $\backslash delta\; =\; 0$ (where $\backslash delta\; \backslash equiv\; \backslash rho\; -\; 1$). Since the test is done over the residual term rather than raw data, it is not possible to use standard t-distribution to provide critical values. Therefore this statistic $t$ has a specific distribution simply known as the Dickey–Fuller table. There are three main versions of the test: 1. Test for a unit root: :: $\backslash nabla\; y\_t\; =\backslash delta\; y\_+u\_t\; \backslash ,$ 2. Test for a unit root with drift: :: $\backslash nabla\; y\_t\; =a\_0+\backslash delta\; y\_+u\_t\; \backslash ,$ 3. Test for a unit root with drift and deterministic time trend: :: $\backslash nabla\; y\_t\; =\; a\_0+a\_1t+\backslash delta\; y\_+u\_t\; \backslash ,$ Each version of the test has its own critical value which depends on the size of the sample. In each case, the null hypothesis is that there is a unit root, $\backslash delta\; =\; 0$. The tests have low statistical power in that they often cannot distinguish between true unit-root processes ($\backslash delta\; =\; 0$)and near unit-root processes ($\backslash delta$ is close to zero). This is called the "near observation equivalence" problem. The intuition behind the test is as follows. If the series $y$ is stationary (or trend stationary), then it has a tendency to return to a constant (or deterministically trending) mean. Therefore large values will tend to be followed by smaller values (negative changes), and small values by larger values (positive changes). Accordingly, the level of the series will be a significant predictor of next period's change, and will have a negative coefficient. If, on the other hand, the series is integrated, then positive changes and negative changes will occur with probabilities that do not depend on the current level of the series; in a random walk, where you are now does not affect which way you will go next. It is notable that :: $\backslash nabla\; y\_t\; =a\_0\; +\; u\_t\; \backslash ,$ may be rewritten as :: $y\_t\; =\; y\_0\; +\; \backslash sum\_^t\; u\_i\; +\; a\_0t$ with a deterministic trend coming from $a\_0t$ and a stochastic intercept term coming from $y\_0\; +\; \backslash sum\_^t\; u\_i$, resulting in what is referred to as a ''stochastic trend''. There is also an extension of the Dickey–Fuller (DF) test called the augmented Dickey–Fuller test (ADF), which removes all the structural effects (autocorrelation) in the time series and then tests using the same procedure. 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「Dickey–Fuller 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.