應用ARIMA與GARCH模式於台灣運輸產業股價之預測

Abstract

藉由預測可以得知未來可能變化，提供決策者資訊上的參考。本研究使用定量分析，應用時間序列中ARIMA (Autoregressive Integrated Moving Average； Box & Jenkins，1976)模式分析法，以及實證上最常使用的ARCH (Autoregressive Conditional Heteroscedasticity；Engle，1982)模式與GARCH (Generalized Autoregressive Conditional Heteroscedasticity；Bollerslev，1986)模式於台灣運輸產業的股票價格，期能達到良好預測績效，並做不同模式預測能力的比較。

傳統上一般線性迴歸之基本假設，為殘差具有白噪音(White noise)的統計性質，但實證研究已發現許多總體經濟與財務的變數資料，皆與自身前幾期變數或與殘差項有關，且呈現非定態(Non-Stationary)時間序列的特性，因而有了ARIMA(p,d,q)模式，且過去的文獻也發現許多財務與經濟的時間序列，具有高狹峰分配(Leptokurtic)與波動叢聚(Volatility Clustering)的現象，這與一般常態分配和變異數不隨時間變化的性質不同，因而有了GARCH模式。

本研究將就1999~2006共八年間，既有的台灣加權指數運輸類股股價的公開資訊日資料，依據不同類股的股價，將其取對數之差呈股價報酬率，若非定態則以差分方式平穩化時間序列後，建構出預測模式，再將模式的預測值與2007年間的觀測值做比較，預測績效的指標由相關統計指標驗證，且做運輸類四家個股，在不同模式的股價預測能力比較。 研究發現考量異質變異數的AR(1)-GARCH(1,1)模式，在該類股具有異質變異的特性時，較原先的AR(1)模式能提高預測能力，且當預測期間引入2008年，研究建構的模式仍然有很好的預測能力。

關鍵字：時間序列、ARIMA、GARCH、股價預測

From forecast we may know the possible changes in the future, providing information references for policy-makers. This research use quantitative analysis, applying time series models to stock price forecasting of transportation industry in Taiwan. We apply the Autoregressive Integrated Moving Average models proposed by Box& Jenkins(1976) and various volatility models, namely, the Autoregressive Conditional Heteroscedasticity(ARCH) models proposed by Engle(1982) and Generalized ARCH proposed by Bollerslev(1986). We expect to achieve good forecast results and compare the predictive ability of different models. The traditional linear regressions assume that residuals have the white noise statistical nature. But the empirical studies have discovered that many financial and economic data, are not independent among returns of nearby days. These data have the non-stationary time series characteristic and leptokurtic and volatility clustering. The property can be explained by changes through time in volatility. The non-normal distribution assumption of GARCH model can successfully capture these general properties of returns. We found that AR(1) model and AR(1)-GARCH(1,1) model are appropriate to investigate empirically the statistical attributes of daily stock price changes from 1999 to 2006 in Taiwan’s transportation industries. And the latter has the good predictive ability, but different models on different stocks do not have uniform result. When out-of-sample change, the models still to have good predictability.

Keywords: time series、ARIMA model、GARCH model、stock price forecast