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A Test Against Spurious Long Memory

  • Qu, Zhongjun

This paper proposes a test statistic for the null hypothesis that a given time series is a stationary long-memory process against the alternative hypothesis that it is affected by regime change or a smoothly varying trend. The proposed test is in the frequency domain and is based on the derivatives of the profiled local Whittle likelihood function in a degenerating neighborhood of the origin. The assumptions used are mild, allowing for non-Gaussianity or conditional heteroscedasticity. The resulting null limiting distribution is free of nuisance parameters and can be easily simulated. Furthermore, the test is straightforward to implement; in particular, it does not require specifying the form of the trend or the number of different regimes under the alternative hypothesis. Monte Carlo simulation shows that the test has decent size and power properties. The article also considers three empirical applications to illustrate the usefulness of the test. This article has supplementary material online.

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Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 29 (2011)
Issue (Month): 3 ()
Pages: 423-438

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Handle: RePEc:bes:jnlbes:v:29:i:3:y:2011:p:423-438
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  1. Smith, Aaron D., 2004. "Level Shifts and the Illusion of Long Memory in Economic Time Series," Working Papers 11974, University of California, Davis, Department of Agricultural and Resource Economics.
  2. Shao, Xiaofeng & Wu, Wei Biao, 2007. "Local Whittle Estimation Of Fractional Integration For Nonlinear Processes," Econometric Theory, Cambridge University Press, vol. 23(05), pages 899-929, October.
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  10. Juan J. Dolado & Jesus Gonzalo & Laura Mayoral, 2005. "What is What? A Simple Time-Domain Test of Long-memory vs. Structural Breaks," Working Papers 258, Barcelona Graduate School of Economics.
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  12. Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
  13. Giraitis, Liudas & Leipus, Remigijus & Philippe, Anne, 2006. "A Test For Stationarity Versus Trends And Unit Roots For A Wide Class Of Dependent Errors," Econometric Theory, Cambridge University Press, vol. 22(06), pages 989-1029, December.
  14. Katsumi Shimotsu, 2006. "Simple (but effective) tests of long memory versus structural breaks," Working Papers 1101, Queen's University, Department of Economics.
  15. Federico Bandi & Benoit Perron, 2003. "Long memory and the relation between implied and realized volatility," Econometrics 0305004, EconWPA.
  16. Ørregaard Nielsen, Morten, 2004. "Local empirical spectral measure of multivariate processes with long range dependence," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 145-166, January.
  17. Beran, Jan & Feng, Yuanhua, 2002. "SEMIFAR models--a semiparametric approach to modelling trends, long-range dependence and nonstationarity," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 393-419, August.
  18. Sibbertsen, Philipp & Venetis, Ioannis, 2003. "Distinguishing between long-range dependence and deterministic trends," Technical Reports 2003,16, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  19. Hurvich, Clifford & Lang, Gabriel & Soulier, Philippe, 2005. "Estimation of Long Memory in the Presence of a Smooth Nonparametric Trend," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 853-871, September.
  20. Wu, Wei Biao & Shao, Xiaofeng, 2007. "A Limit Theorem For Quadratic Forms And Its Applications," Econometric Theory, Cambridge University Press, vol. 23(05), pages 930-951, October.
  21. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
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