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Some tests for unit roots in seasonal time series with deterministic trends. (English) Zbl 0764.62070

Summary: Using the Lagrange multiplier principle, we develop test statistics for testing seasonal unit roots in a time series with possible deterministic trends. The asymptotic distributions of the test statistics are derived: they are functionals of stochastic integrals of standard Brownian bridges. Empirical percentiles of the test statistics for selected seasonal periods are provided.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics
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[1] Ahn, S. K., Lagrange multiplier test for unit roots in ARIMA models with deterministic trends, Manuscript (1992), Dept. of Management and Syst., Washington State Univ: Dept. of Management and Syst., Washington State Univ Pullman, WA
[2] Barsky, R. B.; Miron, J. A., The seasonal cycle and the business cycle, J. Polit. Econom., 97, 503-534 (1989)
[3] Bhargava, A., On the theory of testing for unit roots in observed time series, Rev. Econom. Stud., 52, 384-396 (1986) · Zbl 0602.62074
[4] Chan, N. H.; Wei, C. Z., Limiting distribution of least squares estimates of unstable autoregressive processes, Ann. Statist., 16, 367-401 (1988) · Zbl 0666.62019
[5] Dickey, D. A.; Fuller, W. A., Distribution of the estimators for autocorrelated time series with a unit root, J. Amer. Statist. Assoc., 74, 427-431 (1979) · Zbl 0413.62075
[6] Dickey, D. A.; Fuller, W. A., Likelihood ratio test statistics for autoregressive time series with a unit root, Econometrica, 49, 1057-1072 (1981) · Zbl 0471.62090
[7] Dickey, D. A.; Hasza, D. P.; Fuller, W. A., Testing for unit roots in seasonal time series, J. Amer. Statist. Assoc., 79, 355-367 (1984) · Zbl 0559.62074
[8] Durbin, J., Distribution Theory for Tests Based on the Sample Distribution Function (1973), SIAM: SIAM Philladelphia, PA · Zbl 0267.62002
[9] Hall, A., Testing for a unit root in the presence of moving average errors, Biometrika, 76, 49-56 (1989) · Zbl 0678.62083
[10] Hylleberg, H.; Engle, R. F.; Granger, C. W.J.; Yoo, B. S., Seasonal integration and co-integration, J. Econometrics, 44, 215-238 (1990) · Zbl 0709.62102
[11] Johansen, S., Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models, Econometrica, 59, 1551-1580 (1991) · Zbl 0755.62087
[12] Nankervis, J. C.; Savin, N. E., Finite sample distributions of \(t\) and \(F\) statistics, Econometric Theory, 3, 387-408 (1987) · Zbl 0658.62140
[13] Nelson, C. R.; Plosser, C. I., Trend versus random walks in macroeconomic time series: Some evidences and implications, J. Monetary Econom., 10, 139-162 (1982)
[14] Phillips, P. C.B., Time series regression with unit roots, Econometrica, 55, 277-301 (1987) · Zbl 0613.62109
[15] Phillips, P. C.B.; Perron, P., Testing for a unit root in time series regression, Biometrika, 75, 335-346 (1988) · Zbl 0644.62094
[16] Said, S. E.; Dickey, D. A., Testing for unit roots in autoregressive moving average models for unknown order, Biometrika, 71, 599-608 (1984) · Zbl 0564.62075
[17] Schmidt, P.; Phillips, P. C.B., Testing for a unit root in the presence of deterministic trends, Manuscript (1989), Michigan State Univ: Michigan State Univ East Lansing, MI
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