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タイトル: | Unit root tests considering initial values and a concise method for computing powers |
著者: | Hitomi, Kohtaro Jin, Jianwei Nagai, Keiji Nishiyama, Yoshihiko Tao, Junfan |
キーワード: | Dickey-Fuller tests Squared Bessel process joint density powers approximated by normal distribution exact distribution C12 C22 C46 |
発行日: | Nov-2022 |
出版者: | Institute of Economic Research, Kyoto University |
誌名: | KIER Discussion Paper |
巻: | 1084 |
開始ページ: | 1 |
終了ページ: | 20 |
抄録: | The Dickey-Fuller (DF) unit root tests are widely used in empirical studies on economics. In the local-to-unity asymptotic theory, the effects of initial values vanish as the sample size grows. However, for a small sample size, the initial value will affect the distribution of the test statistics. When ignoring the effect of the initial value, the left-sided unit root test sets the critical value smaller than it should be. Therefore, the size and power of the test become smaller. This paper investigates the effect of the initial value for the DF test (including the t test). Limiting approximations of the DF test statistics are the ratios of two integrals which are represented via a one-dimensional squared Bessel process. We derive the joint density of the squared Bessel process and its integral, enabling us to compute this ratio's distribution. For independent normal errors, the exact distribution of the Dickey-Fuller coefficient test statistic is obtained using the Imhof (1961) method for non-central chi-squared distribution. Numerical results show that when the sample size is small, the limiting distributions of the DF test statistics with initial values fit well with the exact or simulated distributions. We transform the DF test with respect to a local parameter into the test for a shift in the location parameter of normal distributions. As a result, a concise method for computing the powers of DF tests is derived. |
記述: | This research was supported by the 2018 Kyoto University Institute of Economic Research Joint Usage and Research Center Project “Asymptotic Theory of Sequential Tests and Estimation of Unit Root Processes” |
URI: | http://hdl.handle.net/2433/277734 |
関連リンク: | https://www.kier.kyoto-u.ac.jp/publication/?cat=en |
出現コレクション: | KIER Discussion Paper (英文版) |
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