Abstract
This paper considers model selection and forecasting issues in two closely related models for nonstationary periodic autoregressive time series [PAR]. Periodically integrated seasonal time series [PIAR] need a periodic differencing filter to remove the stochastic trend. On the other hand, when the nonperiodic first order differencing filter can be applied, one can have a periodic model with a nonseasonal unit root [PARI]. In this paper, we discuss and evaluate two testing strategies to select between these two models. Furthermore, we compare the relative forecasting performance of each model using Monte Carlo simulations and some U.K. macroeconomic seasonal time series. One result is that forecasting with PARI models while the data generating process is a PIAR process seems to be worse thanvice versa.
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References
Boswijk, H.P. & Franses, P.H. (1994) Unit Roots in Periodic Autoregressions, Tinbergen Institute discussion paper TI 94-4, Rotterdam.
Box, G.E.P. & Jenkins, G.M. (1970)Time Series Analysis, Forecasting and Control, San Francisco: Holden-Day.
Davidson, R. & MacKinnon, J.G. (1993)Estimation and Inference in Econometrics, New York: Oxford University Press.
Franses, P.H. (1994) A Multivariate Approach to Modelling Univariate Seasonal Time Series,Journal of Econometrics, 63, 133–152.
Franses, P.H. & Paap, R. (1994) Model Selection in Periodic Autoregressions,Oxford Bulletin of Economics and Statistics, 56, 421–439.
Fuller, W.A. (1976)Introduction to Statistical Time Series, New York: Wiley.
Ghysels, E. & Hall, A. (1993) On Periodic Time Series and Testing the Unit Root Hypothesis, Discussion paper 2693, C.R.D.E., University of Montreal.
Gladyshev, E.G. (1961) Periodically Correlated Random Sequences,Soviet Mathematics, 2, 385–388.
Hylleberg, S., Engle, R.F., Granger, C.W.J. & Yoo, B. (1990) Seasonal Integration and Cointegration.Journal of Econometrics, 44, 215–238.
Lütkepohl, H. (1991)Introduction to Multiple Time Series Analysis, Berlin: Springer-Verlag.
McLeod, A.I. (1993) Parsimony, Model Adequacy and Periodic Correlation in Time Series Forecasting,International Statistical Review, 61, 387–393.
Osborn, D.R. (1988) Seasonality and Habit Persistence in a Life-Cycle Model of Consumption,Journal of Applied Econometrics, 3, 255–266.
Osborn, D.R. (1990) A Survey of Seasonality in UK Macroeconomic Variables,International Journal of Forecasting, 6, 327–336.
Osborn, D.R. & Smith, J.P. (1989) The Performance of Periodic Autoregressive Models in Forecasting Seasonal U.K. Consumption,Journal of Business and Economic Statistics, 7, 117–127.
Vecchia, R.L. & Ballerini, R. (1991) Testing for Periodic Autocorrelations in Seasonal Time Series Data,Biometrika, 78, 53–63.
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This research was sponsored by the Economic Research Foundation, which is a part of the Netherlands Organization for Scientific Research (N.W.O.). The first author thanks the financial support from the Royal Netherlands Academy of Arts and Sciences. Part of the material in this paper has been presented at seminars at Tulane University and Brown University Several discussions with Eric Ghysels and Hahn Lee proved to be very helpful. Comments from an anonymous referee are gratefully acknowledged.
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Franses, P.H., Paap, R. Periodic integration: further results on model selection and forecasting. Statistical Papers 37, 33–52 (1996). https://doi.org/10.1007/BF02926158
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DOI: https://doi.org/10.1007/BF02926158