近年來，由於經濟市場的快速成長，使得投資組合愈來愈受到重視。在實務上，往往利用具時間序列的模型來對股價進行模型配適，以達到預測的效果。但由於現今經濟市場存在太多影響因素，因此學者們紛紛提出許多的模型來配適股價的動態，而隨機波動模型與門檻隨機波動模型為兩種近來常被討論的模型。
本文以門檻隨機波動模型，利用經驗貝氏方法建立經驗貝氏模型，其動機在於當資料來源無法在上述兩模型間做一確認時，經驗貝氏模型可做為一折衷。另外也考慮風險值 (VaR) 之預測，分別對隨機波動模型、門檻隨機波動模型及經驗貝氏模型進行比較。結果顯示經驗貝氏模型不僅具有較穩健的預測能力，也大大的降低了選模錯誤的風險。

Berger, J.O. (1985). Statistical decision theory and Bayesian analysis，2nd Edition . New York: Springer-Verlag .
Black, F. and Scholes, M. (1973). “The pricing of option and corporate liabilities.” Journal of Political Economy, 81, 637-654.
Black, F. (1976). “Studies of stock price volatility changes.” Proceedings of the American Statistical Association, Business and Economic Statistics Section, 177-181.
Bollerslev, T. (1986). “Generalized autoregressive conditional heteros- kedasticity.” Journal of Econometrics, Vol.31, 307-327.
Carlin, B.P. and Louis, T.A. (2000). “Bayes and empirical Bayes methods for data analysis. ” New York: Chapman and Hall.
Casella, G. (1985). “An introduction to empirical Bayes data analysis.” The American Statistician, 39, 83-87.
Chang, Y.P., Hung, M.C. and Wu, Y.F. (2003). “Nonparametric estimation for risk in Value-at-Risk estimator.” Communications In Statistics:Simulation and Computation, 32, 1041-1064.
Christie, A. (1982). “The stochastic behaviour of common stock variances: value, leverage and interest rate effects.” Journal of Financial Economics, 10, 407-432.
Engle, R.F. (1982). “Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation.” Econometrica, 50, 987-1008.
Geman, S. and Geman, D. (1984). “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images.” IEEE Trans. On Pattern Analysis and Machine Intelligence, 6, 721-741.
Harvey, A.C. and Shephard, N. (1993). “Estimation and testing of stochastic variance models.” STICERD Econometrics Discussion Paper, LSE.
Harvey, A.C., Ruiz, E. and Shephard, N. (1994). “Multivariate stochastic variance model.” Review of Economic Studies, 61, 247-264.
Harvey, A.C. and Shephard, N. (1996). “Estimation of an asymmetric stochastic volatility model for asset returns,” Journal of Business and Statistics, 14, 429-434.
Jacquier, E., Polson, N.G. and Rossi, P.E. (1994). “Bayesian analysis of stochastic volatility models.” Journal of Business and Economic Statistics, 12, 371-389.
Jorion, P. (1997). “Value at Risk: The New Benchmark for Controlling Market Risk.” New York: McGraw-Hill.
Kim, S., Shephard, N. and Chib, S. (1998). “Stochastic volatility: likelihood inference and comparison with ARCH models.” Review of Economic Studies, 65, 361-393.
Lam, K., Li, W.K. and Wong, P.S. (1990). “Price changes and tradingvolume relationship in the Hong Kong stock market.” Asia Pacific Journal of Management, 7, 25-42.
Li, W.K. and Lam, K. (1995). “Modelling asymmetry in stock returns by a threshold ARCH model.” The Statistician, 44, 333-341.
Markowitz (1952). “Portfolio Selection.” Journal of Finance,7,77-91
Morris, C.N. (1983a). “Parametric empirical Bayes inference: Theory and applications.” Journal of the American Statistical Association, 78, 47-65.
Morris, C.N. (1983b). “Natural exponential families with quadratic variance functions: Statistical theory.” Annals of Statistics, 11, 515-529.
Pitt, M.K. (1997). Bayesian Inference for Non-Gaussian State Space Models. Unpublished DPhil thesis, Faculty of Mathematical Sciences, University of Oxford.
Pitt, M.K. and Shephard, N. (1999). “Time varying covariances: a factor stochastic volatility approach (with discussion).” In Bayesian Statistics 6, Proceedings of the Sixth Valencia International Meeting, Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds). Oxford University Press: Oxford; 547-570.
Ridder, T. (1997), “Basic of statistical VaR-estimation.” In: Bol, D., Nakhaeizadeh, G., Vollmer, K. H., eds. Risk Measurement, Econometrics and Neural Networks. Heidelberg: Physica-Verlag. 161-187.
Robbins, H. (1955). “An empirical Bayes approach to statistics.” In Proceedings of 3rd Berkeley Symp. Mathematical Statistics and Probability, 1, Berkeley, CA: Univ. of California Press, 157-164.
Schwert, G.W. (1989). “Why does stock market volatility change over time ?” Journal of Finance, 44, 1115-1153.
Shephard, N. (1993). “Fitting nonlinear time-series models with applications to stochastic variance models.” Journal of Applied Econometrics, 8, S135-S152.
Shephard, N. (1994). “Partial non-Gaussian state space.” Biometrika, 81, 115-131.
So, M.K.P., Lam, K. and Li, W.K. (1997 a). “An empirical study of volatility of seven southeast Asian stock markets using ARV models.” Journal of Business Finance & Accounting, 24, 261-275.
So, M.K.P., Li, W.K. and Lam, K. (1997 b). “Multivariate modelling of the autoregressive random variance process.” Journal of Time Series Analysis, 18, 429-446.
So, M.K.P., Lam, K. and Li, W.K. (1998). “A stochastic volatility model with Markov switching.” Journal of Business and Economic Statistics, 16, 244-253.
So, M.K.P., Li, W.K. and Lam, K. (2002). “A Threshold Stochastic Volatility Model.” Journal of Forecasting, 21, 473-500.
Taylor, S.J. (1982). “Financial returns modelled by the product of two stochastic processes, a study of daily sugar prices 1961-79.” In Time Series Analysis: Theory and Practice 1, Anderson OD (ed.). North-Holland: Amsterdam; 203-226.
Taylor, S.J. (1986). Modelling Financial Time Series, John Wiley: New York.
Taylor, S.J. (1994). “Modelling stochastic volatility.” Mathematical Finance, 4, 183-204.