本文主要有兩個目的，其一是將延續McCabe and Smith (1998) 去探討McCabe and Tremayne (1995) 統計式(MT 統計式) 的檢定力，修改其文中隨機係數與誤差此兩變數不相關的假設。其二是從McCabe and Smith (1998)文中可以發現理論假設與模擬過程兩者不同，因此導致兩者有不一致的現象。在隨機係數與誤差此兩變數為同期相關的假設下導出了MT 統計式在對立下的極限分配。研究結果發現在此兩變數有相關下MT 統計式必須再除以樣本數的四分之一次方才足以收斂到一個期望值為零的分配，因此兩變數在有相關下，MT 統計式將會是以一個變異數趨近無窮大的方式發散。MT 統計式的檢定力雖然會隨著樣本數增加而增加，但增加有限。此外，此兩變數的相關性和隨機係數本身的變異數對檢定力為正影響。最後本文將以原理論假設下去重新模擬McCabe and Smith (1998) 的理論，重新模擬後的結果與其理論預期之結果一致。

In this thesis, I relax McCabe and Smith (1998)’s assumptions to reconsider the power properties of McCabe and Tremayne (1995, MT) test for the difference stationarity of a times series. Without the independence assumption between the random coefficient and error process as that of McCabe and Smith (1998) , I derive the asymptotic distribution of MT test under local heteroscedastic integration alternative. I find that the MT test statistics is O(T1/4) and therefore it is diverge. In a finite sample, the power increase as the correlation or the variance of error process increase. Monte Carlo evidence supports our theoretical findings.

口試委員會審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
第一章緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
第一節研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
第二節研究動機與目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
第三節研究架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
第二章文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第一節傳統單根檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第二節隨機單根檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
第一小節虛無假設. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
第二小節對立假設. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
第三章當隨機係數與誤差相關時McCabe and Tremayne (1995) 統計式的檢定力. 15
第一節模型設定與假設. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
第二節理論推導. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
第四章蒙地卡羅(Monte Carlo) 模擬. . . . . . . . . . . . . . . . . . . . . . . . . . 20
第五章結論與建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
附錄A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
附錄B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
附錄C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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