單根檢定一直是時間序列資料分析中的重要議題。本篇論文以Distaso (2008)的ALM統計式為基礎，使隨機係數和誤差項具有同期相關性，推導ALM統計式在對立假設下的極限分配以及該統計式使用蒙地卡羅模擬下，得到的檢定力。研究發現，在隨機係數和誤差項具有同期相關性下，ALM統計式需除以樣本數的二分之一才收斂到極限分配，所以當樣本數的增加，ALM統計式的檢定力將隨之增加，理論與模擬的結論相互符合。另外發現到無論是隨機係數與誤差項的相關係數還是隨機係數的變異數的增加，同樣會使ALM統計式的檢定力增加。

Unit root test has always been an important issue in time series data analysis. Based on the ALM test of Distaso (2008), this paper makes the random coefficient and the error term have the correlation, derives the limit distribution of the ALM test under the alternative hypothesis and uses Monte Carlo simulation to verification.
The study found that under the correlation between random coefficients and error terms, the ALM test needs to be divided by two-thirds of the sample number to converge to the limit distribution, so when the number of samples increases, the power of ALM test will increases.
In addition, it is found that both the correlation coefficient of the random coefficient and the error term or the variance of the random coefficient increase, which also increases the power of the ALM test.

論文審定書 i
摘要ii
Abstract iii
第一章 緒論1
1.1 研究動機與目的 1
1.2 研究架構 2
第二章 文獻回顧 3
2.1 傳統的單根模型 3
2.2 隨機單根模型6
第三章 研究方法 11
3.1 模型設定與假設檢定11
3.2 ALM 統計式在對立假設下的極限分配14
第四章 蒙地卡羅模擬法 19
4.1 模擬過程 19
4.2 模擬結果 20
第五章 結論24
參考文獻 25
附錄 A 26
附錄 B 28

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