自我迴歸模型之參數估計漸近特性研究

The asymptotic properties of estimates of the parameters in autoregressive

李嘉桓(Chia-Huan Li)

指導教授 ： 蘇南誠

國立臺北大學/商學院/統計學系/碩士(2015年)

摘要

本論文中,探討非常態誤差項的自我迴歸模型,且令誤差項服從 Azzalini (1985) 的偏斜常態分配及 Bondon (2009) 的微偏斜常態分配兩種情形。分別推導了其動差估計量,最小平方估計量與最大概似估計量,然後推論其漸近特性。並且用蒙地卡羅法模擬模型參數的估計表現,最後利用此模型到真實的時間序列資料上,並觀察不同模型與真實資料的配適狀況。

關鍵字

自我迴歸模型 ； 微偏斜常態分配 ； 偏斜常態分配 ； 非常態誤差項

並列摘要

In the modelling of non-Gaussian time series, one strategy is to retain the general autoregressive moving average (ARMA) framework and allow the white noise to be non-Gaussian distribution. In this work, we are interested in correlated data exhibiting asymmetry by adopting a non-Gaussian autoregressive model with Azzalini's (1985) skew-normal distribution and Bondon's (2009) epsilon-skew-normal innovations. The moments estimate, least squares estimate and conditional maximum likelihood estimates of the parameters are derived, and their limit distributions are proved. For small sample behavior, we assess the performance of proposed methods through Monte Carlo simulations. Finally, the flexibility of this model is illustrated by fitting it to a real time series.

並列關鍵字

autoregressive models ； epsilon-skew-normal distribution ； skew-normal distribution

參考文獻

Bondon, P. (2009). Estimation of autoregressive models with epsilon-skewnormal innovations. Journal of Multivariate Analysis, 100(8):1761{1776.

Brockwell, P. J. and Davis, R. A. (2009). Time series: theory and methods. Springer Science & Business Media.

Genton, M. G. (2004). Skew-elliptical distributions and their applications: a journey beyond normality. CRC Press.

Hutson, A. (2004). Utilizing the fexibility of the epsilon-skew-normal distribution for common regression problems. Journal of Applied Statistics, 31(6):673-683.

Lo, A. W. and Newey, W. K. (1985). A large-sample chow test for the linear simultaneous equation. Economics Letters, 18(4):351-353.