| Abstract: | 時間序列分析中平穩線型模式之模式選取(Model selection)問題,也就是ARMA(p,q)模式中p與q的選取,一直是個重要且困難的主題,因此吸引了許多統計學者與經濟學者的注意,而致力於這方面的研究。自Box與Jenkins (1970)提出以ACF及PACF作為選模的方法後,即不斷地有新的選模準則被提出或對現有的準則作進一步的修正,其中較著名者有Akaike(1977)的AIC(An information criterion),Schwarz(1978)與Rissanen(1978)的BIC(Bayesian information criterion)以及Hannen與Quinn(1979)的HQ Criterion以及Pukkila et al.(1990)所提出的選模方法(以下簡稱PKK選模法)。 近年來,有關非平穩模式與雙線型模式的模式選取問題也漸漸受到重視,而有各種方法的提出,如針對非平穩模式的Dickey-Fuller(DF)單位根檢定,Subba Rao(1981)的巢狀搜尋選模法。本文藉模擬資料分析來比較上述各種選模法之選模能力,並歸訥出:若序列之真實模式非平穩時,宜先以Dickey-Fuller(DF)單位根檢定決定差分次數後,再以PKK選模法決定p、q的值;對於雙線性模式,則以Subba Rao(1981)的巢狀搜尋選模法之選模能力最佳。此外,我們也從貝氏統計觀點提出自回歸模式的選模法,並以模擬資料驗證其選模能力。
The problem of model selection for stationary linear time series models has been an attractive but difficult one in time series analysis in the past twenty years. Several criteria were raised and justified. These include AIC (An Information Criterion) raised by Akaike (1977), BIC (Bayesian Information Criterion) by Schwarz (1978) and Rissanen (1978). HQ criterion by Hannen & Quinn (1979) and the PKK method, suggested by Pukkila et al. (1990). Recently, there have been a lot of researchers working on model selection problem for nonstationary or nonlinear (bilinear, in particular) models, several criteria such as Dickey-Fuller (1977)`s unit root test for nonstationary models, Subba Rao (1981)` nested search procedure for bilinear models are suggested and used. In this article, we compare the performance of the above model selection criteria both for nonstationary and bilinear models using simulated data. It is found that when the true model is nonstationary, unit root test together with PKK method would provide the best performance. On the other hand, when the true model is bilinear, Subba Rao`s nested search procedure gives better results than PKK method, AIC or BIC criteria did. A Bayesian model selection procedure for autoregressive models is also suggested and evaluated through Monte Carlo method. |
