臺灣博碩士論文加值系統

隨著時間序列的發展，在模型鑑定上出現了許多圖形特徵辨識法(Pattern Identification Method)，例如S-Array和R-Array法，GPAC法，ESACF法以及角落表法(Corner Method)等等。這些方法，都有著比AIC、BIC等傳統利用懲罰因子(Penalty Factor)作模型鑑定方法運算上更為簡單容易的優點，此外，這些利用圖形特徵來判斷模型階次，是更容易讓人清楚判斷的。　　
角落表法是其中少數可以使用在轉換函數模型的圖形特徵辨識法。原始是由Beguin, Gourieroux, 和Monfort(1980)所提出針對一ARMA(p,q)序列作模型鑑定的方法。Liu和Hassens(1982)則將此法推廣使用在多元輸入序列的轉換函數，主要是利用最小平方法在輸出入序列上，利用求得的迴歸係數估計式來產生模型鑑定的表格。雖然在上述的研究中表列了作為模型鑑定依據的表格特徵，但是文中並未詳加證明該特徵是否一定成立，此外，對於表格中的元素是否為零究竟應該如何檢定，作者也未提出相關的理論敘述。這些檢定上未知的統計特性，也成了在使用角落表法上讓人不放心的地方。　　
為了更加了解角落表法，本研究首先證明了原始文獻中的表格特徵成立，接著採用了重複模擬的方式，讓不同的轉換模型參數、模擬次數以及不同的誤差項假設互相配對組合，在給定的已知模型下，去觀察利用角落表法所產生的表格元素的平均數以及變異數，在多次的模擬後，觀察其表格元素的表現是否與所證明出的表格特徵相符合。　　
經由模擬結果的比較分析，利用重複模擬的方式得到的元素變異數估計值，在用來對表格元素作檢定時具有一定程度的效果，檢定出的結果與表格理論特徵相吻合。雖然在表格尾端有變異數稍微高估的現象，但不影響整體的檢定結果。

Pattern identification methods have been widely used for determining the order of an ARMA process, such as S-Array and R-Array Method、GPAC Method and ESACF Method. Compared with penalty function identification methods, the pattern identification methods are computationally cheap. Corner method is also one of the pattern identification methods. Most important, it can be used for transfer-noise function model.
Corner method was proposed by Beguin, Gourieroux, and Monfort in 1980. In 1982, Liu and Hassens used the least square method to find the estimates of the regression coefficients and produce an array to determine the order of a multiple-input transfer function. It still has the advantages mentioned above. However, Liu and Hassens neither proved the patterns of the array nor proposed a test procedure on their article. This study wants to know more about the unknown statistical properties of corner method.
Since the asymptotic distribution of the test statistics of the array is difficult to be derived, we use repeating simulation to find the variance of the elements and use them to be variance estimates to test each element in the array. Given different parameters、numbers of simulation and error term models, we inspect that if the results of the simulation and the theory are coincident. Also, the patterns of the array are also proved in the research.
According to the results of the simulation, we find that it almost can determine the true model in different kinds of situations, which means the variance calculated from repeating simulation is well-behaved. Although it seems to be over estimated in the tail of the array, the results of the model identification aren’t affected too much.

目錄
第一章 緒論﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒1
第一節 背景與動機﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒1
第二節 研究目的﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒2
第二章 文獻回顧﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒4
第一節 R-Array 和 S-Array法﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒4
第二節 GPAC法 ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒7
第三節 ESACF法﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒9
第四節 角落表法 ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒11
第三章 研究方法﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒13
第一節 應用於轉換函數模型鑑定的角落表法 ﹒﹒﹒﹒﹒﹒﹒﹒13
第二節 角落表法中 特徵之證明﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒17
第三節 角落表法 中元素之檢定﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒22
第四節 重複模擬設計﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒24
第四章 模擬流程與實例探討﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒27
第一節 模擬介紹 ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒27
第二節 模擬結果 ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒30
第三節 實例分析 ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒36
第五章 結論與建議﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒39
附錄一 殘差項為白噪音假設下符號表格之整理﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒42
附錄二 殘差項為MA(1)假設下符號表格之整理﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒48
附錄三 殘差項為白噪音假設下之模擬結果﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒54
附錄四 殘差項為MA(1)假設下之模擬結果﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒68
附錄五 實例分析結果之列表﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒82
附錄六 程式碼﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒84
參考文獻 ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒87
表目錄
表2-1 S-array產生的特徵表格﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒6
表2-2 R-array產生的特徵表格﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒6
表2-3 GPAC法產生的特徵表格﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒8
表2-4 ESACF法產生的特徵表格 ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒10
表2-5 角落表法產生的特徵表格 ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒12
表3-1 角落表法使用於轉換函數模型鑑定產生之特徵表格﹒﹒15
表4-1 模擬模型列表﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒28
表4-2 使用重複模擬方式於角落表法之選模結果﹒﹒﹒﹒﹒﹒﹒31
表4-3 以模式17模擬產生的符號表格(誤差項為白噪音模型模擬次數
n=100) ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒32
表4-4 模式11模擬產生之結果(誤差項為白噪音模型，模擬次數
n=100) ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒33
表4-5 表4-4所對應的符號表格 ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒33
表4-6 模式2模擬產生的符號表格(誤差項為白噪音模型，模擬次數
n=30) ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒34
表4-7 模式2模擬產生的符號表格(誤差項為MA(1)模型，模擬次數
n=30) ﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒34
表4-8 模式14模擬產生的符號表格(誤差項為MA(1)模型，模擬次
n=30)﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒35
表4-9 模式14模擬產生的符號表格(誤差項為MA(1)模型，模擬次
n=500)﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒35

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