具多變量t自相關誤差的時間數列迴歸模型

Abstract

本篇論文考慮具自迴歸多變量t誤差的線性迴歸模型的貝氏方法，它的條件變異數滿足了GARCH模型的一種型式。在沒有訊息的先驗分配下，我們提出了近似貝氏的後驗方法與預測的推論。我們也運用馬可夫鏈蒙地卡羅去更精確地計算後驗分配。為提高計算上的效率，我們提供了一個求具AR(p)過程的自相關矩陣之反矩陣的快速計算方法。最後我們用一個美國利率的實例來闡述我們所提出的方法。

This thesis considers a Bayesian approach to the regression model with autoregressive multivariate t errors, whose conditional variance satis‾es a kind of generalized autoregressive conditional heteroscedastic model. We present the approximate Bayesian posterior and predictive inferences under a non-informative prior. Markov chain Monte Carlo computational schemes are developed for precisely accounting for the posterior uncertainties. To enhance the computational e±ciency, we provide a fast method to compute the inverse autocorrelation matrix of an AR(p) process. A real example of the U.S. interest rates is conducted to demonstrate our methodologies.