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Numerical distribution functions for seasonal unit root tests

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  • Diaz-Emparanza, Ignacio

Abstract

It is often necessary to test for the presence of seasonal unit roots when working with time series data observed at intervals of less than a year. One of the most widely used methods for doing this is based on regressing the seasonal difference of the series over the transformations of the series by applying specific filters for each seasonal frequency. This provides test statistics with non-standard distributions. A generalisation of this method for any periodicity is presented and a response surface regressions approach is used to calculate the P-values of the statistics whatever the periodicity and sample size of the data. The algorithms are prepared with the Gretl open source econometrics package and two empirical examples are presented.

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  • Diaz-Emparanza, Ignacio, 2014. "Numerical distribution functions for seasonal unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 237-247.
    • Handle: RePEc:eee:csdana:v:76:y:2014:i:c:p:237-247
    DOI: 10.1016/j.csda.2013.03.006
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    1. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    2. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    3. Juha Ahtola & George C. Tiao, 1987. "Distributions Of Least Squares Estimators Of Autoregressive Parameters For A Process With Complex Roots On The Unit Circle," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(1), pages 1-14, January.
    4. Serena Ng & Pierre Perron, 2005. "A Note on the Selection of Time Series Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(1), pages 115-134, February.
    5. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    6. Osborn, Denise R, et al, 1988. "Seasonality and the Order of Integration for Consumption," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 50(4), pages 361-377, November.
    7. Franses, P. H., 1990. "Testing For Seasonal Unit Roots In Monthly Data," Econometric Institute Archives 272393, Erasmus University Rotterdam.
    8. Canova, Fabio & Hansen, Bruce E, 1995. "Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 237-252, July.
    9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    10. Harvey, David I. & van Dijk, Dick, 2006. "Sample size, lag order and critical values of seasonal unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2734-2751, June.
    11. Marsaglia, George & Tsang, Wai Wan, 2000. "The Ziggurat Method for Generating Random Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i08).
    12. Joseph Beaulieu, J. & Miron, Jeffrey A., 1993. "Seasonal unit roots in aggregate U.S. data," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 305-328.
    13. John Conlisk, 1974. "Optimal Response Surface Design in Monte Carlo Sampling Experiments," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 3, pages 463-473, National Bureau of Economic Research, Inc.
    14. Giovanni Baiocchi, 2007. "Reproducible research in computational economics: guidelines, integrated approaches, and open source software," Computational Economics, Springer;Society for Computational Economics, vol. 30(1), pages 19-40, August.
    15. Yalta, A. Talha & Schreiber, Sven, 2012. "Random Number Generation in gretl," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(c01).
    16. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    17. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    18. Hertel, Ida & Kohler, Michael, 2013. "Estimation of the optimal design of a nonlinear parametric regression problem via Monte Carlo experiments," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 1-12.
    19. MacKinnon, James G, 1996. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 601-618, Nov.-Dec..
    20. MacKinnon, James G, 1994. "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 167-176, April.
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    1. Tomás Barrio Castro & Andrii Bodnar & Andreu Sansó, 2017. "Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending," Computational Statistics, Springer, vol. 32(4), pages 1533-1568, December.
    2. Díaz-Emparanza Herrero, Ignacio & Moral Zuazo, María Paz, 2013. "Seasonal Stability Tests in gretl. An Application to International Tourism Data," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).

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