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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 ADF-GLS test ： ウィキペディア英語版 ADF-GLS test In statistics and econometrics, the ADF-GLS test (or DF-GLS test) is a test for a unit root in an economic time series sample. It was developed by Elliott, Rothenberg and Stock (ERS) in 1992 as a modification of the augmented Dickey–Fuller test (ADF). A unit root test determines whether a time series variable is non-stationary using an autoregressive model. For series featuring deterministic components in the form of a constant or a linear trend then ERS developed an asymptotically point optimal test to detect a unit root. This testing procedure dominates other existing unit root tests in terms of power. It locally de-trends (de-means) data series to efficiently estimate the deterministic parameters of the series, and use the transformed data to perform a usual ADF unit root test. This procedure helps to remove the means and linear trends for series that are not far from the non-stationary region.〔(Efficient Tests for an Autoregressive Unit Root, Elliott, Rothenberg and Stock, Econometrica Vol. 64, No. 4, pp. 813-836, Jul., 1996 )〕 == Explanation == Consider a simple time series model $y\_=d\_t+u\_\backslash ,$ with $u\_=\backslash rho\; u\_+e\_\backslash ,$ where $d\_t\backslash ,$ is the deterministic part and $u\_\backslash ,$ is the stochastic part of $y\_\backslash ,$. When the true value of $\backslash rho\; \backslash ,$ is close to 1, estimation of the model, i.e. $d\_t\backslash ,$ will pose efficiency problems because the $y\_\backslash ,$ will be close to nonstationary. In this setting, testing for the stationarity features of the given times series will also be subject to general statistical problems. To overcome such problems ERS suggested to locally difference the time series. Consider the case where closeness to 1 for the autoregressive parameter is modelled as $\backslash rho=1-\backslash frac\; \backslash ,$ where $T\; \backslash ,$ is the number of observations. Now consider filtering the series using $1-\backslash fracL\; \backslash ,$ with $L\; \backslash ,$ being a standard lag operator, i.e. $\backslash bar\_t=y\_t-(\backslash bar/T)y\_\; \backslash ,$. Working with $\backslash bar\_t\; \backslash ,$ would result in power gain, as ERS show, when testing the stationarity features of $y\_t\; \backslash ,$ using the augmented Dickey-Fuller test. This is a point optimal test for which $\backslash bar\; \backslash ,$ is set in such a way that the test would have a 50 percent power when the alternative is characterized by $\backslash rho=1-c/T\; \backslash ,$ for $c=\backslash bar\; \backslash ,$. Depending on the specification of $d\_t\; \backslash ,$, $\backslash bar\; \backslash ,$ will take different values. 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「ADF-GLS 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.