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Long memory and stochastic trend

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  • Leipus, Remigijus
  • Viano, Marie-Claude

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.

Suggested Citation

  • Leipus, Remigijus & Viano, Marie-Claude, 2003. "Long memory and stochastic trend," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 177-190, January.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:2:p:177-190
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    Cited by:

    1. 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.
    2. 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.
    3. Gary Biglaiser & Ching-to Albert Ma, 2007. "Moonlighting: public service and private practice," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1113-1133, December.
    4. YAMAMOTO, Yohei & 山本, 庸平, 2015. "Asymptotic Inference for Common Factor Models in the Presence of Jumps," Discussion Papers 2015-05, Graduate School of Economics, Hitotsubashi University.
    5. Pierre Perron & Yohei Yamamoto, 2016. "On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests," Econometric Reviews, Taylor & Francis Journals, vol. 35(5), pages 782-844, May.
    6. Surgailis, Donatas & Teyssière, Gilles & Vaiciulis, Marijus, 2008. "The increment ratio statistic," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 510-541, March.
    7. 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.
    8. Yoon, Gawon, 2005. "Long-memory property of nonlinear transformations of break processes," Economics Letters, Elsevier, vol. 87(3), pages 373-377, June.
    9. Chevillon, Guillaume, 2016. "Multistep forecasting in the presence of location shifts," International Journal of Forecasting, Elsevier, vol. 32(1), pages 121-137.
    10. 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.
    11. 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.
    12. 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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