時間序列中對於模式階數的選取，一直是重要的課題。從過去文獻研究得

知，大多數的討論都局限於平穩的模式。然而近年來，非平穩型序列逐漸

成為各學者研究的方向。因此，一個能協助研究者適當處理資料的方法，

如採取適當的單位根檢定，是進行實證分析時所必需採行的程序。在本篇

文章中我們是採用單位根檢定來決定差分階數，然後再結合 Pukkila et

al.(1990)所提出的選模方法決定p、q的階數(簡稱PKK選模法)經由本文模

擬結果所得之結論為當序列為平穩型時，直接用PKK選模法來進行階數的

選取，能得到較強的選模能力 。但當序列為非平穩型時，則建議先以單

位根檢定來決定差分階數，再佐以PKK選模法決定p、q階數。

Agiakloglou, C. and Newbold, P. (1992), "En1pirical Evidence on DickeyFuller
Tests," ]ouTnal of Ti'me SeTies Analysis, 6, 471-483.
Box, G. E. P., and Jenkins, G. Nt (1976), Ti'me SeTies Analysis:Forecasting
and Control, 2nd ed, San Francisco: Holden-Day.
Choi, B. S. (1992), ARMA 1vlodel Identification) Ne\v York: Springer Verlag.
Dickey, D. A., and Said, S. E (1985) , "Hypothesis Testing in ARlj\;IA(p,l,q)
l\iIodels," ] ournal of the A m,erican Statistical Association, 80 , 369-374.
Dickey, D. A., and Bell, vV, R. and IvIiller, R. B. (1986), "Unit Root in Tin1e
Series NIodels:Tests and hnplications," The A'meTican Statistician, 40,12-26.
Dickey, D. A., and Pantula. S. G. (1987) , " Detern1ining the Order of Differencing
in Autoregressi\'e Processes," ]o'uTnal of B'ussiness and Econo'mic
Statistics, 5, 455-461.
Dickey, D. A., and Fuller, W .A. (1979), "Distribution of the Estilnation for
Autoregressive Time Series \.Vith a Unit Root :" ]o'uTnal of the A'merican
Statistical Association ,74, 427-431.
--( 1981), "Likelihood Ration Statistics for Autoregressive Tin1e Series
with A Unit Root," Econo'metTica, 49, 1057-1073.
Fuller, W. A. (1976), Intorduction to Statistical Time Series, New York:Wiley.
--(1985), "Nonstationary Autoregressive Time Series ," Handbook of
Statistics , 5, 1-23.
Hasza, D. P., and Fuller, W. A. (1979), "Estimation for Autoregressive
Process with Unit Roots,” The Annals of Statistics, 7, 1106-1120.
Koreisha,S.,and Pukkila,T.(1990),”A Generalized Least-Squares Approach for Estimation of Autoregressive Moving-Average Models,” Journal of Time Series Analysis, 11, 139-151.
Koreisha,S.,and Yoshimoto,G.(1991),”A Comparision among Identification Procedures for Autoregressive Moving Average Models,” International Statistical Review, 59, 37-57.
Pagan, A.R. and Wicken, M.R. (1989), “A Survey of Some Recent Econometric Methods,” The Economic Journal , 962-1025.
Pantula,S.G.(1989),”Testing for Unit Root in Time Series Data”, Econometric Theory , 5, 256-271.
Phillips.P.C.B.(1987),”Time Series Regression with Unit Roots,”Econometrica, 55, 277-302.
Phillips,P.C.B.,and P.Perron. (1988),”Testing for a Unit Root in Time Series Regression.” Biometrika, 75, 335-346.
Pukkila,T., and Koreisha,S., and Kallinen,A. (1990),”The identification of ARMA Models,” Biometrika, 77, 537-548.
Pukkila, T.M.,and Krishnaiah,P.R.(1988),”On the Use of Autoregressive Order Determination Criteria in Univariate White Noise Tests,” IEEE Transaction on Acoustics, Speech, and , Signal Processing, 36, 764-774.
Said,E.D., and Dickey ,D.A. (1984),”Testing for Unit Roots in Autoregressive Moving Avreage Models of Unknow Order,” Biometrika, 71, 599-607.
Schwert, G.W. (1987),”Effects of Model Specification on Tests for Unit Roots in Macroecomic Data,” Journal of Monetary Economics, 20, 73-103.
--------(1989), “Tests for Unit Roots: A Monte Carlo Investigation,” Journal of Bussiness and Economic Statistics, 7, 147-159.
Solo, V.(1984),”The Order of Differencing in ARIMA Models,” Journal of the American Statistical Association, 79, 916-921.
Wei, Willian W.S. (1990), Time Series Analysis: Univariate and Multivariate Methods,New York:Addison –Wesley.