轉換函數為時間序列分析之一大主軸，是以一動態模式解釋說明解釋變數與反應變數之間的關係。目前僅有Box與Jenkins(1976)所提出的交叉相關函數方法及Liu與Hanssens(1982)所提出的線性轉換函數法可對轉換函數進行模式鑑定。可見尋找一轉換函數模型鑑定法，仍然為一值得研究之議題。
在建構轉換模式之後吾人常以AIC、BIC及H&Q等傳統模式選擇準則選模。然而AIC準則在樣本數大的情況下，常會有高估的情形發生且參數並未達到一致性估計；BIC準則雖不會有高估或低估階次之情形，但參數並未達到一致性及有效性估計；H&Q 準則的參數估計式為強一致收斂，但於樣本小時會有低估階次之情形。由定義可知，以上幾項傳統模式選擇準則的懲罰因子並未完全考量到隱藏於資料分配內的潛在重要因子。有鑑於此，Chen(1993)、(1996) 年提出以「重覆抽樣法」分別決定單維度及二元自我迴歸函數之模型階次。從其研究結果發現，使用重覆抽樣法所得到的階次估計值會弱收斂至真實階次且選階能力也較傳統的模式選擇準則佳。
眾知，轉換函數數為二元自我迴歸函數之特例，因此本研究將探討轉換函數是否亦能使用重覆抽樣法鑑定其模式及建立一模式選擇準則。本研究結果發現：理論方面，由類似Durbin-Levinson Algorithm 證明方式可證得轉換函數的預測誤差平方和為一遞減函數。在此前題之下，方能建立一模式選擇準則。本研究據此更進一步由連續對映性質證得轉換函數使用重覆抽樣法選階所得之階次估計會弱收斂至模型的真實階次；然而模擬結果方面，本研究所提出的方法在轉換函數模型階次較低時，有較高的選階能力；而當樣本數較大時，選階能力亦會提高。因此整體而言，本研究的選階準確率雖低於其他傳統選模準則，但仍然提供讀者一項新穎的模式選擇方式。
關鍵字：轉換函數模型、二元自我迴歸函數、重覆抽樣法、

Transform Function is one topic of time series analysis. Up to the present day, we only have two methods to identify the Transform Function. One is Cross Correlation Function (CCF) which is proposed by Box & Jenkins (1976) and the other is Linear Transform Function (LTF) which is proposed by Lin & Hanssens (1982). Therefore, looking for the new identification method for Transform Function is the reworded-dicsussing subject.
After constructing the Transform function model, we always use traditional criterion ,such as AIC、BIC and H&Q for model selection. However, AIC criterion always overfit and parameter estimator is not consistency for large sample size ,and BIC criterion is not consistency efficiency, and H&Q criterion always underfit for small sample size. For above defects, Chen et al.(1993) proposed Resampling methods for determining the order of autoregressive process.
As we know, Transform Function is a special case of bivariate autoregression function. Therefore, in this thesis we extend the results of Chen(1996) for multivariate autoregressive processes using resampling methods to the Transform Function.
In this paper, we prove the mean square error of prediction is monotone decreasing. Under this prerequisite, we can build the model selection criterion and prove the Yule-Walker estimators of the resampling test series are weak consistency.
In simulation aspect, our method will have good choice for large sample size or low order.
Key words: Transform Function、Resampling method、AIC

目錄
第一章 緒論 1
第一節 轉換函數模型………………………… ………1
第二節 模式選擇準則… ………………………………2
第三節 重覆抽樣方法……… ………………………………3
第四節 研究動機與研究介紹…… …………………………4
第二章 基礎理論與文獻探討 6
第一節 基礎理論………………………… ……………6
第二節 文獻探討……………………………………………15
第三章 使用重覆抽樣法估計轉換函數模型階次 24
第一節 理論證明………………………………………24
第二節 模擬流程………………………………………38
第三節 轉換函數雜訊項為 模型之探討………………… 41
第四章 模擬結果 40
第五章 研究結論與後續建議 43
附錄一…………………………………………………………45
附錄二…………………………………………………………46
參考文獻 58
圖目錄
圖1-1 研究架構圖……………………………………………5
表目錄
表4-1 轉換函數滿足4-1式之模擬結果……………………41
表4-2 轉換函數滿足4-2式之模擬結果……………………41
表4-3 轉換函數滿足4-3式之模擬結果……………………41
表4-4 二元自我迴歸函數滿足4-1式之模擬結果…………42
表4-5 二元自我迴歸函數滿足4-2式之模擬結果…………42
表4-6 二元自我迴歸函數滿足4-3式之模擬結果…………42
附表1a…………………………………………………………45
附表1b…………………………………………………………45
附表1c…………………………………………………………45
附表1d…………………………………………………………45
附表2a…………………………………………………………46
附表2b…………………………………………………………46
附表2c…………………………………………………………46

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