Abstract
This paper analyzes the nature of seasonal fluctuations in quarterly observations for Austrian consumption and income data. We begin with univariate tests of the order of integration and then move on to tests of cointegration. Seasonally adjusted as well as raw data are used in these tests. in univariate tests, the outcome for seasonally adjusted and raw data is in line. The unit roots at the zero frequency found in the seasonally adjusted series are also present in the raw data. In bivariate tests, the results for seasonally adjusted and raw data differ. While we find cointegration at the zero frequency between consumption and income for seasonally adjusted series, this hypothesis is generally rejected for the raw data.
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References
Burridge P, Wallis KF (1984) Unobserved-components models for seasonal adjustment filters. Journal of Business and Economic Statistics 2:350–359
Cleveland WP, Tiao GC (1976) Decomposition of seasonal time series: A model for the Census X-11 program. Journal of the American Statistical Association 71:581–587
Dickey DA, Pantula SG (1987) Determining the order of differencing in autoregressive processes. Journal of Economic and Business Statistics 5:455–461
Doornik JA, Hendry DF (1994) PcGive 8.0. An interactive econometric modelling system. International Thomson Publishing, London
Engle RF, Granger CWJ, Hallman J (1989) Merging short- and long-run forecasts: An application of seasonal cointegration to monthly electricity sales forecasting. Journal of Econometrics 40:45–62
Franses PH, Hylleberg S, Lee HS (1995) Spurious deterministic seasonality. Economics Letters 48:249–256
Ghysels E (1993) On the economics and econometrics of seasonality. In: Sims CA (ed.) Advances in Econometrics, Cambridge University Press, Cambridge
Ghysels E, Perron P (1993) The effect of seasonal adjustment filters on tests for a unit root. Journal of Econometrics 55:56–99
Ghysels E, Lee HS, Noh J (1994) Testing for unit roots in seasonal time series. Some theoretical extensions and a Monte Carlo investigation. Journal of Econometrics 62:415–442
Hylleberg S (1992) Modelling seasonality. Oxford University Press, Oxford
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
Kunst RM (1993) Seasonal cointegration in macroeconomic systems: Case studies for small and large European countries. Review of Economics and Statistics LXXV:325–330
Lee HS (1992) Maximum likelihood inference on cointegration and seasonal cointegration. Journal of Econometrics 54:1–47
Lee HS, Siklos PL (1993) The influence of seasonal adjustment on the Canadian consumption function. Canadian Journal of Economics XXVI:575–589
Lee HS, Siklos PL (1995) A note on the critical values for the maximum likelihood (seasonal) cointegration tests. Economics Letters 49:137–145
MacKinnon JG (1991) Critical values for cointegration tests. In: Engle RF, Granger CWJ (eds.) Long-run economic relationships, Oxford University Press, Oxford:267–276
Maravall A (1993) Unobserved components in economic time series. Forthcoming in: Pesaran H, Schmidt P, Wickens M (eds.) The handbook of applied econometrics, Vol. 1, Basil Blackwell, Oxford
McDougall RS (1995) The seasonal unit root structure in New Zealand macroeconomic variables. Applied Economics 27:817–827
Osborn DR (1990) A survey of seasonality in UK macroeconomic variables. International Journal of Forecasting 6:327–336
Osborn DR, Chui APL, Smith JP, Birchenhall CR (1988) Seasonality and the order of intergration for consumption. Oxford Bulletin of Economics and Statistics 50:361–377
Osterwald-Lenum M (1992) A note with quantiles of the asymptotic of the ml cointegration rank test statistics. Oxford Bulletin of Economics and Statistics 54:461–472
Perron P (1988) Trends and random walks in macroeconomic time series. Journal of Economic Dynamics and Control 12:297–332
Sims CA (1974) Seasonality in regression. Journal of the American Statistical Society 69:618–627
Wallis KF (1974) Seasonal adjustment and relations between variables. Journal of the American Statistical Society 69:18–31
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Han, L., Thury, G. Testing for seasonal integration and cointegration: The Austrian consumption income relationship. Empirical Economics 22, 331–344 (1997). https://doi.org/10.1007/BF01208827
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DOI: https://doi.org/10.1007/BF01208827