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A Test Against Spurious Long Memory

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  • Zhongjun Qu

    ()
    (Department of Economics, Boston University)

Abstract

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 a¤ected 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 heteroskedasticity. The resulting null limiting distribution is nuisance parameter free and can be easily simulated. Furthermore, the test is straightforward to implement. In particular, it does not require one to specify the form of the trend or the number of di¤erent regimes under the alternative hypothesis. Monte Carlo simulation shows that the test has decent size and power properties. The paper also considers three empirical applications to illustrate the usefulness of the test.

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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2010-051.

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Length: 49 pages
Date of creation: Jan 2010
Date of revision:
Handle: RePEc:bos:wpaper:wp2010-051

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References

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  1. Ulrich Mueller & Mark W. Watson, 2006. "Testing Models of Low-Frequency Variability," NBER Working Papers 12671, National Bureau of Economic Research, Inc.
  2. 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.
  3. Smith, Aaron, 2005. "Level Shifts and the Illusion of Long Memory in Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 321-335, July.
  4. Katsumi Shimotsu, 2006. "Simple (but effective) tests of long memory versus structural breaks," Working Papers 1101, Queen's University, Department of Economics.
  5. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
  6. 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.
  7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
  8. 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.
  9. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-67, July.
  10. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  11. 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.
  12. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-68, July.
  13. Deo, Rohit & Hurvich, Clifford & Lu, Yi, 2006. "Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 29-58.
  14. 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.
  15. 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.
  16. Federico Bandi & Benoit Perron, 2003. "Long memory and the relation between implied and realized volatility," Econometrics 0305004, EconWPA.
  17. 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.
  18. 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.
  19. Bent Jesper Christensen & Morten Ørregaard Nielsen, 2007. "The Effect of Long Memory in Volatility on Stock Market Fluctuations," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 684-700, November.
  20. Pierre Perron & Zhongjun Qu, 2008. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Boston University - Department of Economics - Working Papers Series wp2008-004, Boston University - Department of Economics.
  21. 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.
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Citations

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Cited by:
  1. Grassi, Stefano & Santucci de Magistris, Paolo, 2014. "When long memory meets the Kalman filter: A comparative study," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 301-319.
  2. Eduardo Rossi & Paolo Santucci de Magistris, 2009. "Long Memory and Tail dependence in Trading Volume and Volatility," CREATES Research Papers 2009-30, School of Economics and Management, University of Aarhus.
  3. Philip Bertram & Robinson Kruse & Philipp Sibbertsen, 2013. "Fractional integration versus level shifts: the case of realized asset correlations," Statistical Papers, Springer, vol. 54(4), pages 977-991, November.
  4. Pierre Perron & Yohei Yamamoto, 2011. "Estimating and Testing Multiple Structural Changes in Linear Models Using Band Spectral Regressions," Boston University - Department of Economics - Working Papers Series WP2011-049, Boston University - Department of Economics.
  5. Adam McCloskey, 2013. "Estimation of the long-memory stochastic volatility model parameters that is robust to level shifts and deterministic trends," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 285-301, 05.
  6. Uwe Hassler & Antonio Rubia & Paulo M.M. Rodrigues, 2014. "Persistence in the Banking Industry: Fractional integration and breaks in memory," Working Papers w201406, Banco de Portugal, Economics and Research Department.

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