本文的主要目的，是延續探討Su and Roca (2012) 的結果，其中Lee 統計式的
誤差項與隨機係數的相關性會導致檢定力有所變化。我們使用McCabe and Smith
(1998) 局部異質對立假設的方式並加入了隨機係數與誤差的相關係數，導出在此
條件之下的分配，並發現這分配是以樣本數的四分之一次方的速度發散，在這樣
的情況下樣本數增加會使檢定力增加，我們再從分配結果觀察誤差項與隨機係數
的相關性也會有一樣的效果，並在模擬做驗證。在結果可以看出其發散效果主要
是以變異數方散到無限大的形式發生。這在隨機係數的變異數相對小時，對立下
的分配發散會導致檢定力增加，但並不會使檢定力到1。而在隨機係數的變異數
相對大時例如檢定力到1 時，此發散效果反而會使得檢定力反而下降。

The main purpose of this paper is to continue to explore the results of Su and Roca
(2012).The correlation between the error term and the random coefficient of Lee’s statistical
formula will lead to a a change in the verification force.We use the methodof partial
heterogeneity hyprothsis of McCabe and Smith(1988) and join the correlation coefficient
between the random coefficient and the error is derived,and the distribution is derived.It is
found that the distribution is divergent at the rate of one quarter of the number of samples.
Under such allocation,the increase of the number of samples will increase the verification
force ,and observe the distribution result.The correction between the error term and the
random coefficient will have the same effect,and the simulation will be carried out in the
simulation.It can be seen that the divergence effent mainly occours in the form of the variance
number,which leads to an increase in the verification force,but the increase is limited.
Keywords: stochastic unit root (STUR) test; Wiener process; the sequence of local alternatives;
weak convergence; difference stationary.
iii

口試委員會審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
圖次. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
表次. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
第一章緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
第一節研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
第二節研究目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
第三節研究架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
第二章文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第一節單根檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第一小節單根模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第二小節ADF 檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
第三小節PP 檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
第二節隨機單根. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
第一小節隨機單根模型. . . . . . . . . . . . . . . . . . . . . . . . . . . 9
第二小節隨機單根檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . 10
第三小節對立假設下分配. . . . . . . . . . . . . . . . . . . . . . . . . 12
第三章隨機係數與誤差相關時Lee (1998) 統計式檢定力. . . . . . . . . . . . 15
第一節模型設立與假設. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
第二節理論與推導. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
第四章蒙地卡羅模擬. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
第五章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
附錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
第一節證明1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
第二節證明2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
第三節證明3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
第四節證明4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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