Abstract
Seasonal cointegration generalizes the idea of cointegration to processes with unit roots at frequencies different from 0. Here, “common seasonals,” also a dual notion of common trends, is adopted for the seasonal case. The features are demonstrated in exemplary models for German and U.K. data. An evaluation of the predictive value of accounting for seasonal cointegration shows that seasonal cointegration may be difficult to exploit to improve predictive accuracy even in cases where seasonal non-cointegration is clearly rejected on statistical grounds. The findings from the real-world examples are corroborated by Monte Carlo simulation.
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References
Bell WR (1987) A note on overdifferencing and the equivalence of seasonal time series models with monthly means and models with (0, 1, 1)12 seasonal parts when φ=1. Journal of Business and Economic Statistics 5:383–387
Brandner P, Kunst RM (1990) Forecasting vector autoregressions — the influence of cointegration. Research Memorandum No 265, Institute for Advanced Studies, Vienna
Chatterjee S, Ravikumar B (1992) A neoclassical model of seasonal fluctuations. Journal of Econometrics 29:59–86
Engle RF, Granger CWJ (1987) Co-integration and error correction: representation, estimation and testing. Econometrica 55:251–276
Engle RF, Granger CWJ, Hallman JJ (1989) Merging short-and long-run forecasts: An application of seasonal cointegration to monthly electricity sales forecasting. Journal of Econometrics 40:45–62
Engle RF, Yoo BS (1987) Forecasting and testing in co-integrated systems. Journal of Econometrics 35:143–159
Franses PH (1991) Seasonality, non-stationarity and the forecasting of monthly time series. International Journal of Forecasting 7:199–208
Franses PH, Kloek T (1991) A periodic cointegration model of quarterly consumption in Austria and Japan. Paper presented at the ESEM, Cambridge
Ghysels E (1990) Unit-root tests and the statistical pitfalls of seasonal adjustment: The case of US postwar real gross national product. Journal of Business and Economic Statistic 8:145–152
Gonzalo J, Granger CWJ (1991) Estimation of common long-memory components in cointegrated systems. Discussion Paper 91-33, University of California, San Diego
Hylleberg S, Engle RF, Granger CWJ, Yoo BS (1990) Seasonal integration and cointegration. Journal of Econometrics 44:215–238
Johansen S (1988) Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12:231–254
Johansen S (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59:1551–1580
Johansen S (1992) Estimating systems of trending variables. Mimeo, University of Copenhagen
Joyeux R (1992) Tests for seasonal cointegration using principal components. Journal of Time Series Analysis 13:109–118
Kasa K (1992) Common stochastic trends in international stock markets. Journal of Monetary Economics 29:95–154
Kunst RM (1993) Seasonal cointegration in macroeconomic systems: Case studies for small and large European economies. To appear in Review of Economics and Statistics
Lee HS (1992) Maximum likelihood inference on cointegration and seasonal cointegration. Journal of Econometrics 54:1–48
Lee HS, Siklos P (1991) Unit roots and seasonal unit roots in macroeconomic time series: Canadian Evidence. Economics Letters 35:273–277
Miron JA, Zeldes SP (1988) Seasonality, cost shocks and the production smoothing model of inventories. Econometrica 56:877–908
Osborn DR (1988) Seasonality and habit persistence in a life cycle model of consumption. Journal of Applied Econometrics 3:255–266
Osborn DR (1990a) The implications of periodically varying coefficients for seasonal time-series processes. Journal of Econometrics 48:373–384
Osborn DR (1990b) A survey of seasonality in UK macroeconomic variables. International Journal of Forecasting 6:327–336
Plosser CI (1979) Short-term forecasting and seasonal adjustment. Journal of the American Statistical Association 74:15–24
Reimers HE (1991) Analyse kointegrierter Variablen mittels vektorautoregressiver Modelle (Analysis of cointegrated variables by means of vector autoregressive models). Physica-Verlag, Heidelberg (in German)
Stock JH, Watson MW (1988) Testing for common trends. Journal of the American Statistical Association 83, 404:1097–1107
Wallis KF (1982) Seasonal adjustment and revision of current data: Linear filters for the X-11 method. Journal of the Royal Statistical Society A 145:74–85
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Part of this paper was written while the author was visiting professor at the University of California San Diego.