偏斜常態自我迴歸模型之參數估計研究

Estimation of autoregressive models with skew-normal innovations

黃思齊(Ssu-Chi Huang)

指導教授 ： 蘇南誠

國立臺北大學/商學院/統計學系/碩士(2014年)

摘要

本篇論文中，我們利用偏斜常態分佈作為自我迴歸模型的非常態誤差項，建立一個新的模型，其中推導了其參數的動差估計量與最大概似估計量，並利用模擬的方法觀察參數估計量的大樣本性質。最後，我們利用此模型和其他模型去配適道瓊的股票指數，去觀察此模型對資料的配適情況。

關鍵字

動差 ； 偏斜常態分佈 ； 非常態誤差項 ； 條件最大概似估計量

並列摘要

In the modelling of non-Gaussian time series, one strategy is to retain the general autoregressive moving average framework and allow the white noise to be non-Gaussian. In this work, we are interested in correlated data exhibiting asymmetry by adopting a non-Gaussian autoregressive model with Azzalini's skew normal innovations. The moments and conditional maximum likelihood estimators of the parameters are derived, and their limit distributions are studied by Monte Carlo simulation. Finally, the flexibility of this model is illustrated by fitting it to a real time series.

並列關鍵字

moments ； skew-normal ； non-Gaussian innovation ； conditional maximum likelihood estimation

參考文獻

Andel, J. (1988). On AR(1) processes with exponential white noise. Com-

Scandinavian journal of statistics, pages 171–178.

Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multi-

Series B (Statistical Methodology), 61(3):579–602.

Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal dis-