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Long memory and stochastic trend

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  • Leipus, Remigijus
  • Viano, Marie-Claude
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    Abstract

    In this paper, we study a general stochastic trend model and provide conditions on the partial sums which imply the convergence of the V/S statistic. These conditions generalize those in Giraitis et al. (J. Appl. Probab. 38 (2001) 1033) obtained in the case of deterministic trend model. As a particular example of stochastic trend we study a regime switching process called mixture model. We prove that in the non-trivial cases the partial sums converge to a compound Poisson process whereas in "degenerated" cases it resembles the behavior of the I(d-1) process.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 61 (2003)
    Issue (Month): 2 (January)
    Pages: 177-190

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    Handle: RePEc:eee:stapro:v:61:y:2003:i:2:p:177-190

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    Related research

    Keywords: Long memory Stochastic trend Compound Binomial process Compound Poisson process Mixture model;

    References

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    1. Clive W.J. Granger & Namwon Hyung, 2013. "Occasional Structural Breaks and Long Memory," Annals of Economics and Finance, Society for AEF, vol. 14(2), pages 739-764, November.
    2. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus & Teyssiere, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," Journal of Econometrics, Elsevier, vol. 112(2), pages 265-294, February.
    3. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
    4. Engle, Robert F & Smith, Aaron, 1998. "Stochastic Permanent Breaks," University of California at San Diego, Economics Working Paper Series qt99v0s0zx, Department of Economics, UC San Diego.
    5. I.N. Lobato & N.E. Savin, 1996. "Real and Spurious Long Memory Properties of Stock Market Data," Econometrics 9605004, EconWPA, revised 26 Sep 1996.
    6. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    7. Granger, Clive W.J. & Teräsvirta, Timo, 1998. "A simple nonlinear time series model with misleading linear properties," Working Paper Series in Economics and Finance 237, Stockholm School of Economics.
    8. Andersson, Michael K. & Eklund, Bruno & Lyhagen, Johan, 1999. "A simple linear time series model with misleading nonlinear properties," Economics Letters, Elsevier, vol. 65(3), pages 281-284, December.
    9. Gourieroux, Christian & Jasiak, Joann, 2001. "Memory and infrequent breaks," Economics Letters, Elsevier, vol. 70(1), pages 29-41, January.
    10. Liu, Ming, 2000. "Modeling long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 99(1), pages 139-171, November.
    11. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
    12. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September.
    13. William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
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    Citations

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    Cited by:
    1. Aue, Alexander & Horváth, Lajos & Steinebach, Josef, 2007. "Rescaled range analysis in the presence of stochastic trend," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1165-1175, July.
    2. 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.
    3. Gary Biglaiser & Ching-to Albert Ma, 2006. "Moonlighting: Public Service and Private Practice," Working Papers 12, Portuguese Competition Authority.
    4. Pierre Perron & Zhongjun Qu, 2006. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts and its Implications for Stock Returns Volatility," Boston University - Department of Economics - Working Papers Series WP2006-016, Boston University - Department of Economics.
    5. Surgailis, Donatas & Teyssière, Gilles & Vaiciulis, Marijus, 2008. "The increment ratio statistic," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 510-541, March.
    6. Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
    7. Yoon, Gawon, 2005. "Long-memory property of nonlinear transformations of break processes," Economics Letters, Elsevier, vol. 87(3), pages 373-377, June.
    8. Leipus, Remigijus & Paulauskas, Vygantas & Surgailis, Donatas, 2005. "Renewal regime switching and stable limit laws," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 299-327.
    9. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.

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