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題名:非恆定資料下統計推論之穩健性與改善
作者:欉清全 引用關係
校院名稱:國立政治大學
系所名稱:國際貿易學系
指導教授:汪義育
郭炳伸
學位類別:博士
出版日期:2000
主題關鍵詞:單根檢定共積檢定靴帶反覆抽樣法型一誤差扭曲
原始連結:連回原系統網址new window
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本論文主要研究非恆定過程下, 相關檢定量的漸近性質. 並發展一種檢定程序, 使檢定量具有穩健型一誤差表現. 本論文包括三篇文章.
第一篇探討Phillips-Perron檢定量與其類似型式檢定量, 在干擾項為移動平均且參數接近負一設定下的性質.
比較工具變數估計式與簡單迴歸估計式所形成之Phillips-Perron型式檢定量, 我們發現兩者的漸近分配分別以 $ O(\sqrt{T}) $ 與 $ O(T) $
的速度發散; 前者型一誤差表現相對優於後者, 而且增加樣本數並無法改善兩者型一誤差扭曲.
文中接著提出工具變數估計之「修正」型式檢定量, 並導出其漸近分配. 由漸近分配可推論: 大樣本下, 且干擾項為移動平均,
「修正」型式檢定量具有穩健的型一誤差表現. 文中的模擬結果顯示: 即使移動平均干擾項參數接近負一, 且在一般實證常用的樣本數下,
利用「修正」型式檢定量進行靴帶反覆抽樣法, 其型一誤差相當接近事先給定的顯著水準.
第二篇探討恆定檢定量在自迴歸參數設定下的性質. 利用局部化參數的設定方式導出恆定檢定量漸近分配.
由漸近分配型式解釋造成型一誤差扭曲的原因, 同時亦說明檢力的型態. 最後說明靴帶反覆抽樣法改善恆定檢定量型一誤差扭曲的可行性.
雖然Caner \& Kilian (1999)指出, 大樣本下, 當資料來自對立假設, 靴帶反覆抽樣法無法有效重建虛無假設分配, 造成低檢力的問題.
但由模擬結果顯示:在常見的樣本數與總體時間數列資料所對應的參數值下, 靴帶反覆抽樣法可以有效控制恆定檢定量型一誤差,
並且具有良好檢力表現.
最後一篇重新檢視Kuo (1998)所提出「部分共積係數穩定」檢定量之漸近性質. 當截距項為非恆定的特定模型下,
上述檢定量漸近分配事實上異於Kuo (1998)的結果, 並且會以某種速度發散. 由此不僅可以解釋Kuo
(1998)係數穩定檢定量會產生嚴重型一誤差扭曲的模擬結果, 並且可以推論型一誤差表現型態. 文中並以模擬分析驗證理論的結果.
This dissertation analyses asymptotic properties of test statistics when the data generating process is nonstationary.And proposes a test procedure to improve size distortions of the tests.This dissertation includes three articles.
The first article invesigates the asymptotic properties of the Phillips-Perron tests and some of their variants when the error is MA with coefficient close to -1.Asymptotic distributions of the tests described above constructed by IV and OLS estimators diverge with rates of square root of T and T,respectively.
So,the sizes of "IV-type" Phillips-Perron tests are better than those of "OLS-type".And increase sample size can not resolve the size problems. Meanwhile,I propose modified Phillips-Perron tests based on IV estimator.In large samples,the modified tests have robust size.Simulations reveal that when mdified tests are bootstrapped, their sizes are very close to the nominal size
even in small samples.
The second article uses localized parameteralizations to invesigate large sample properties of stationary tests when the DGP is AR.Asymptotic distributions explain
why stationary tests would reject null hypothesis too often when AR root is close to unit.Finally,I discuss the possibility of improving size distrotion
by bootstrap.
The last article investigates the asymptotic property of the test proposed by Kuo (1998).When intercept is I(1), the distribution of the above test is different from that of Kuo (1998). This distribution not only explains the simulation results of Kuo which reveal serious size distrotions of the test but also can infer
the size pattern simultaneously.
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