Translated Titles

Parameter and Interval Estimation For A Positive Autoregressive Process





Key Words

正值自我回歸模型 ; 極值估計 ; 線性規劃估計 ; 厚尾資料 ; 時間序列資料 ; Positive autoregressive processes ; linear programming estimates ; extreme-value estimates ; regular variation indices ; heavy-tailed data



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Chinese Abstract

我們首先研究如何為一階自我回歸模型(Autoregressive Model)之係數構造信賴區間,估計係數所用的估計式為極值估計式。模型干擾項的機率密度函數我們假設為正的且在x趨近於0時,f(x)為b1乘上x的(alpha-1)次方;而當x趨近無窮大時時,f(x)為b2乘上x的(-beta-1)次方, 四個參數b1、b2、alpha以及beta皆為正的且未知的常數,且alpha<beta。在這設定下,極值估計式的極限分配與未知b1及alpha有關,因而無法構造出信賴區間。為解決此難題,我們提出一套嶄新的方法來估計這兩個常數以及證明其具有一致性。這結果不只可以讓我們了解模型下殘差的分配甚至可以讓我們構造出自我回歸模型之係數有效的極限信賴區間,而不需要使用McCormic (1995)的自助抽樣法(bootstrapping)。再來,我們研究在一階自我回歸模型下alpha>beta的情況。用類似上述的估計方法,我們也可以估計b2與beta,且其估計式具有一致性。也就是說,我們可以同時估計b1、b2、alpha以及beta。第三,我們將我們的方法延伸到p階自我回歸模型,在這裡是使用線性規劃估計式來估計模型係數。因為我們用自助抽樣法來處理自我回歸係數的極限分配與p個觀察點的聯合分配有關,而不需要估計b1和b2,所以在p階自我回歸模型下,我們的焦點放在估計alpha和beta。在文獻上,希爾估計式(Hill estimator)在用來估計alpha和beta時有著嚴重的問題,因而我們使用我們的方法可以來同時估計alpha和beta且具有一致性。

Topic Category 社會科學院 > 經濟學研究所
社會科學 > 經濟學
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