# 臺灣博碩士論文加值系統

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 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 presentthe 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.
 Contents1. Introduction .................................32. Approximate Bayesian inference .............. 42.1. The model ....................................42.2. Posterior inference ......................... 72.3. Predictive inference ....................... .93. Markov chain Monte Carlo inference ......... 113.1. Implementation ..............................113.2. Forecasting future values and volatilities...124. An application: the U.S. interest rates......135. Discussion ..................................21
 ReferencesAnderson, T.W. (2003), An Introduction to Multivariate Statistical Analysis (Wiley, 3rd. ed.).Arellano-Valle, R.B., Galea-Rojas, M., Zuazola P.I. (2000), Bayesian sensitivity analysis in elliptical linear regression models. J Statist. Plan. Inference 86, 175-199.Barndor®-Nielsen, O. E., Schou, G. (1973), On the reparameterisation of autoregressive models by partial autocorrelations. J. Multivariate. Anal. 3, 408-419.Bollerslev, T. (1986), Generalized autoregressive conditional heteroscedasticity. J. Econometrics 31, 307-27.Box, G.E.P., Jenkins, G.M., Reinsel, G.C. (1994), Time Series Analysis Forecasting and Control (Holden-Day, San Francisco, 3rd ed.).Brooks, S. P. and Gelman, A. (1998), General methods for monitoring convergence of iterative simulations. J. Comp. Graph. Statist. 7, 434-455.Chen, C.W.S., Lee, J.C., Lee, S.Y., Niu, W.F. (2004), Bayesian estimation for time series regressions improved with exact likelihoods, J. Statist. Comput. Simulation 74, 727 - 740.Chib, S. (1993), Bayes regression with autoregressive errors: A Gibbs sampling approach. J. Econometrics. 58, 275-294.Chib, S., Osiewalski, J., Steel M.F.J. (1991), Posterior inference on degrees of freedom parameters in multivariate-t regression models. Econom Lett. 37, 391-397.Chib, S., Tiwari, R.C., JAMMLAMADAKA (1988), Bayes prediction in regression with elliptical errors. J. Econometrics. 38, 349-360.Engle, R.F. (1982), Autoregressive conditional heteroscedasticity with estimates of variance of United Kingdom in°ation. Econometrica 50, 987-1007.Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B. (2004). Bayesian Data Analysis (Chapman & Hall, New York, 2nd ed.)Kim, H.M., Mallick B.K. (2003), A note on Bayesian spatial prediction using the elliptical distribution. Statist. Probab. Lett. 64, 271-276.Ljung, G.M., Box, G.E.P. (1980), Analysis of variance with autocorrelated obser-vations. Scand. J. Statist. 7, 172-180.Monahan, J.F. (1984), A note on enforcing stationarity in autoregressive moving average models. Biometrika 71, 403-404.Lee, J.C.,Wang, R.S., Lin, T.I. (2004), On the inverse of the autocorrelation matrix for an AR(p) process. J. Chinese Statist. Assoc. 42, 81-89.McCulloch, R.E., Tsay R.S. (1994), Bayesian analysis of autoregressive time series via the Gibbs sampler. J. Time Ser. Anal. 15, 235-250.Osiewalski, J. (1991), A note on Bayesian inference in a regression model with elliptical errors. J. Econometrics 48, 183-193.Osiewalski, J., Steel M.F.J. (1993), Robust Bayesian inference in elliptical models. J. Econometrics 57, 345-363.Singh, R.S. (1988), Estimation of error variance in linear regression models with errors having multivariate student-t distribution with unknown degrees of free-dom. Econom Lett. 27, 47-53.Tarami, B., Pourahmadi M. (2003), Multi-variate t autoregressions: innovations, prediction variances and exact likelihood equation. J. Time Ser. Anal. 24, 739-754.Zellner, A. (1976), Bayesian and non-Bayesian analysis of the regression model with multivariate student-t error terms. J. Amer. Statist. Assoc. 71, 400-405.
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