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Testing for seasonal unit roots by frequency domain regression

Author Info

  • Marcus J. Chambers
  • Joanne S. Ercolani
  • A. M. Robert Taylor

Abstract

This paper develops univariate seasonal unit root tests based on spectral regression estimators. An advantage of the frequency domain approach is that it enables serial correlation to be treated non-parametrically. We demonstrate that our proposed statistics have pivotal limiting distributions under both the null and near seasonally integrated alternatives when we allow for weak dependence in the driving shocks. This is in contrast to the popular seasonal unit root tests of, among others, Hylleberg et al. (1990) which treat serial correlation parametrically via lag augmentation of the test regression. Moreover, our analysis allows for (possibly infinite order) moving average behaviour in the shocks, while extant large sample results pertaining to the Hylleberg et al. (1990) type tests are based on the assumption of a finite autoregression. The size and power properties of our proposed frequency domain regression-based tests are explored and compared for the case of quarterly data with those of the tests of Hylleberg et al. (1990) in simulation experiments.

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File URL: http://www.nottingham.ac.uk/economics/grangercentre/papers/10-02.pdf
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Paper provided by University of Nottingham, Granger Centre for Time Series Econometrics in its series Discussion Papers with number 10/02.

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Date of creation: Sep 2010
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Handle: RePEc:not:notgts:10/02
Contact details of provider: Postal: School of Economics University of Nottingham University Park Nottingham NG7 2RD
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Web page: http://www.nottingham.ac.uk/economics/grangercentre/
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Keywords: Seasonal unit root tests; moving average; frequency domain regression; spectral density estimator; Brownian motion;

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Find related papers by JEL classification:
  • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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  1. Pesaran, H.M. & Timmermann, A., 2003. "How Costly is it to Ignore Breaks when Forecasting the Direction of a Time Series?," Cambridge Working Papers in Economics 0306, Faculty of Economics, University of Cambridge.
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  4. Chambers, Marcus J. & Roderick McCrorie, J., 2007. "Frequency domain estimation of temporally aggregated Gaussian cointegrated systems," Journal of Econometrics, Elsevier, vol. 136(1), pages 1-29, January.
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  7. Castro, Tomás del Barrio & Osborn, Denise R. & Taylor, A.M. Robert, 2012. "On Augmented Hegy Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 28(05), pages 1121-1143, October.
  8. Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2004. "Asymptotic Distributions For Regression-Based Seasonal Unit Root Test Statistics In A Near-Integrated Model," Econometric Theory, Cambridge University Press, vol. 20(04), pages 645-670, August.
  9. Richard Smith & Robert Taylor, . "Additional Critical Values and Asymptotic Representations for Seasonal Unit Root Tests," Discussion Papers 95/43, Department of Economics, University of York.
  10. Hyllerberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988. "Seasonal Integration And Cointegration," Papers 0-88-2, Pennsylvania State - Department of Economics.
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  12. David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2010. "Robust methods for detecting multiple level breaks in autocorrelated time series," Discussion Papers 10/01, University of Nottingham, Granger Centre for Time Series Econometrics.
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  14. J. Joseph Beaulieu & Jeffrey A. Miron, 1992. "Seasonal Unit Roots in Aggregate U.S. Data," NBER Technical Working Papers 0126, National Bureau of Economic Research, Inc.
  15. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  16. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September.
  17. Choi, In & Phillips, Peter C. B., 1993. "Testing for a unit root by frequency domain regression," Journal of Econometrics, Elsevier, vol. 59(3), pages 263-286, October.
  18. Taylor, A M Robert, 2002. "Regression-Based Unit Root Tests with Recursive Mean Adjustment for Seasonal and Nonseasonal Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 269-81, April.
  19. Burridge, Peter & Taylor, A M Robert, 2001. "On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 374-79, July.
  20. Gregoir, Stephane, 2006. "Efficient tests for the presence of a pair of complex conjugate unit roots in real time series," Journal of Econometrics, Elsevier, vol. 130(1), pages 45-100, January.
  21. Ghysels, Eric & Lee, Hahn S. & Noh, Jaesum, 1994. "Testing for unit roots in seasonal time series : Some theoretical extensions and a Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 62(2), pages 415-442, June.
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