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Seasonal integration and cointegration. (English) Zbl 0709.62102
Summary: This paper develops tests for roots in linear time series which have a modulus of one but which correspond to seasonal frequencies. Critical values for the tests are generated by Monte Carlo methods or are shown to be available from critical values of D. A. Dickey and W. A. Fuller [J. Am. Stat. Assoc. 74, 427-431 (1979; Zbl 0413.62075)] or D. A. Dickey, D. P. Hasza and W. A. Fuller [ibid. 79, 355- 367 (1984; Zbl 0559.62074)]. Representations for multivariate processes with combinations of seasonal and zero-frequency unit roots are developed leading to a variety of autoregressive and error-correction representations. The techniques are used to examine cointegration at different frequencies between consumption and income in the U.K.

62P20 Applications of statistics to economics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Full Text: DOI
[1] Ahtola, J.; Tiao, G. C.: Distributions of least squares estimators of autoregressive parameters for a process with complex roots on the unit circle. Journal of time series analysis 8, 1-14 (1987) · Zbl 0618.62088
[2] Barsky, R. B.; Miron, J. A.: The seasonal cycle and the business cycle. Journal of political economy 97, 503-534 (1989)
[3] Bell, W. R.; Hillmer, S. C.: Issues involved with the seasonal adjustment of economic time series. Journal of business and economic statistics 2, 291-320 (1984)
[4] Bhargava, A.: On the specification of regression models in seasonal differences. (1987)
[5] Box, G. E. P.; Jenkins, G. M.: Time series analysis, forecasting and control. (1970) · Zbl 0249.62009
[6] Chan, N. H.; Wei, C. Z.: Limiting distributions of least squares estimates of unstable autoregressive processes. Annals of statistics 16, 367-401 (1988) · Zbl 0666.62019
[7] Davidson, J. E.; Hendry, D. F.; Srba, F.; Yeo, S.: Econometric modelling of aggregate time series relationships between consumer’s expenditure and income in the UK. Economic journal 91, 704-715 (1978)
[8] Dickey, D. A.; Fuller, W. A.: Distribution of the estimators for autoregressive time series with a unit root. Journal of the American statistical association 84, 427-431 (1979) · Zbl 0413.62075
[9] Dickey, D. A.; Hasza, H. P.; Fuller, W. A.: Testing for unit roots in seasonal time series. Journal of the American statistical association 79, 355-367 (1984) · Zbl 0559.62074
[10] Engle, R. F.: On the theory of cointegrated economic time series. U.C.S.D. discussion paper no. 87-26 (1987)
[11] Engle, R. F.; Granger, C. W. J.: Co-integration and error correction: representation, estimation and testing. Econometrica 55, 251-276 (1987) · Zbl 0613.62140
[12] Engle, R. F.; Granger, C. W. J.; Hallman, J.: Merging short- and long-run forecasts: an application of seasonal co-integration to monthly electricity sales forecasting. Journal of econometrics 40, 45-62 (1989)
[13] Fuller, W. A.: Introduction of statistical time series. (1976) · Zbl 0353.62050
[14] Grether, D. M.; Nerlove, M.: Some properties of optimal seasonal adjustment. Econometrica 38, 682-703 (1970)
[15] Hylleberg, S.: Seasonality in regression. (1986) · Zbl 0718.90021
[16] Kailath, T.: Linear systems. (1980) · Zbl 0454.93001
[17] Nelson, C. R.; Plosser, C. I.: Trends and random walks in macroeconomic time series. Journal of monetary economics 10, 129-162 (1982)
[18] Nerlove, M.; Grether, D. M.; Carvalho, J. L.: Analysis of economic time series: A synthesis. (1979) · Zbl 0473.62077
[19] Stock, J. H.: Asymptotic properties of least squares estimates of cointegrating vectors. Econometrica 55, 1035-1056 (1987) · Zbl 0651.62105
[20] Yoo, S.: Co-integrated time series: structure, forecasting and testing. Ph.d. dissertation (1987) · Zbl 0649.62108
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