摘要

一般在處理資料上，常常會受限於所取得的資料是不完整的或是被修正過的，而這樣的行為會導致最終統計推論上的錯誤。故本篇論文利用Gibbs sampling的方式還原出資料被修正的部份且發現無論數列是否為單根，數列模擬的結果均近似真實值。並探討使用被修正的資料與還原過後的資料在單根檢定上的差異，發現到使用被修正的資料在size上比還原過後的為大，而在power上亦較還原的資料為差。最後，以日本貨幣市場的無擔保品利率為實證，發現近幾年此利率有數的月份為0，分析1999年一月到2004年7月的資料。若是直接代入0的資料並以傳統的單根檢定方法，在不考慮平均數的模型下檢定日本的貨幣市場一年期利率為I (0),而利用Gibbs sampling模擬出真實值，代入檢定中發現日本貨幣市場利率亦為I (0)。在考慮平均數的模型之下，日本的貨幣市場一年期利率為I (1),而利用Gibbs sampling模擬出真實值，代入檢定中發現日本貨幣市場利率亦為I

Abstract

Generally speaking, when dealing with some data, our analysis will be limited because of the given data was incompletely or hidden. And these kinds of errors in calculation will arrive at a statistics answer.
This thesis adopts an analysis based on the Gibbs sampling trying to recover the part of hidden data. Since we found out whether time series is unit root or not, the effects of the simulated series will be similar to the true value.
After observing the differences between the hidden data and the recovered data in unit root, we noticed that the hidden data has a bigger size and a weakened power over the recovered data.
Finally, as an example, we give the unsecured loans at the Japanese money market to prove our issues by analyzing the data from January, 1999 to July, 2004. Since we found out that the numerical value of loan is zero at several months these past several years.
In order to observe the Japanese money market, if we substitute the data of zero loan and use the traditional way to inspect unit root without taking model of average value into account, the result will be I(0). And if we simulate the hidden data with Gibbs sampling and substitute the data to inspect the Japanese money market without taking model of average value into account, the result will be I(0) also. But if we take model of average value into account, the of the Japanese Money Market will be I(1). And if we simulate the hidden data with Gibbs sampling and substitute the data to inspect the Japanese money market, the result will be I(I) also.

1 導論 1
2 文獻回顧 4
2.1 Censored Regression Model 4
2.2 Gibbs sampling 8
3 理論模型 11
3.1 條件分配的求導 11
3.2 AR(P)模型之下的截堵模型 15
3.3 模擬抽樣的過程 23
3.4 截堵模型的模擬 26
4 單根檢定 29
4.1 模型的一般化 29
4.2 單根檢定的探討 33
4.3 單根檢定的模擬結果 36
5 實證研究 40
6 結論 43
附表 45
附圖 52
參考文獻 58

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