隨機波動模式(stochastic volatility model)是近來相當受重視的波動率模式，若一報酬率數據服從隨機波動模式，且因政策或量測儀器的限制，而存在截切資料時，常會造成參數估計上的偏誤。有鑑於此，本論文對隨機波動模式下的報酬率數據做函數轉換，使其以autoregressive moving average (ARMA) 模式表示。爾後，採用Park, Genton & Ghosh (2007)提出的在ARMA模式下，截切資料填補演算法進行數據填補與參數估計。此法可避免使用MCMC法對隨機波動模式進行參數估計。此外，此研究也利用訊息矩陣(Fisher information matrices)來評估資料有截切時，參數估計偏誤與效率性。在實證分析上，採用宏達電子(HTC)以及勝華科技的報酬率資料做為實例探討。

Stochastic volatility (SV) model is a popular model for characterizing time-varying variance for return data. Due to some regulation rules in the financial market, observed returns for assets sometimes have truncations. Adapted the idea of Park, Genton and Ghosh (2007) to deal with the truncated data in fitting an ARMA model, this thesis suggests an estimation method to deal with the truncated return data in fitting SV model, which incorporates an imputation step in the maximum likelihood estimation. We demonstrate the efficiency gain of the truncation-adjusted estimator over the unadjusted estimator by comparing their trace of the inverse Fisher information matrices via simulations. The applications to HTC and WINTEK returns are provided for illustration. Keywords: stochastic volatility model, truncated data, ARMA, data augment, estimation, Fisher information matrices.

參考文獻

Box, G. E. P., Jenkins , G. M. & Reinsel, G. C. (1970). Time Series Analysis : Forecasting and Control, 3rd edition.

Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327.

Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflations. Econometrica, 50, 987-1007.

Gourieroux, C.S. & Monfort , A. (1993). Simulation-based inference: A survey with special reference to panel data models. Journal of Econometrics, 59, 5-33.

Harvey, A. C., Ruiz, E. & Shephard, N. (1994). Multivariate stochastic variance models. Review of Economic Studies, 61, 247-264.

Hopke, P. K., Liu, C. & Rubin, D. B. (2001). Multiple imputation for multivariate data with missing and below-threshold measurements : time-series concentrations of
pollutants in the Arctic. Biometrics, 57, 22-33.

Hsieh, P.H. & Yang, J.J. (2009). A censored stochastic volatility approach to the estimation of price limit moves. Journal of Empirical Finance, 16, 337-351.

Jacquier, E., Polson, N. G. & Rossi, P. E. (1994). Bayesian analysis of stochastic volatility models. Journal of Business & Economic Statistics.

Melino & Turnbull, S. M. (1990). Pricing foreign currency options with stochastic volatility. Journal of Econometrics, 45, 239-265.

Nelson, D. B.(1991). Conditional heteroskedasticity in asset returns : A new approach. Econometrica, 59, 347-370.

Park, J. W., Genton, M. G. & Ghosh, S. K. (2007). Censored time series analysis with autoregressive moving average models. Journal of the Canadian Statistics, 35,151-168.

Robinson, P. M.(1980). Estimation and forecasting for time series containing censored or missing observations. Time Series : Proceedings of the International Meeting held at Nottingham University, 167- 182.

Zakoian, J. M. (1994). Threshold heteroskedasticity models. Journal of Economic Dynamics and Control, 18, 931-955.