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Assessing Time-Reversibility Under Minimal Assumptions


  • Zacharias Psaradakis


This article considers a simple procedure for assessing whether a weakly dependent univariate stochastic process is time-reversible. Our approach is based on a simple index of the deviation from zero of the median of the one-dimensional marginal law of differenced data. An attractive feature of the method is that it requires no moment assumptions. Instead of relying on Gaussian asymptotic approximations, we consider using subsampling and resampling methods to construct confidence intervals for the time-reversibility parameter, and show that such inference procedures are asymptotically valid under a mild mixing condition. The small-sample properties of the proposed procedures are examined by means of Monte Carlo experiments and an application to real-world data is also presented. Copyright 2008 The Author. Journal compilation 2008 Blackwell Publishing Ltd

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  • Zacharias Psaradakis, 2008. "Assessing Time-Reversibility Under Minimal Assumptions," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 881-905, September.
  • Handle: RePEc:bla:jtsera:v:29:y:2008:i:5:p:881-905

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    References listed on IDEAS

    1. Racine, Jeffrey S. & Maasoumi, Esfandiar, 2007. "A versatile and robust metric entropy test of time-reversibility, and other hypotheses," Journal of Econometrics, Elsevier, vol. 138(2), pages 547-567, June.
    2. Romano, Joseph P & Wolf, Michael, 2001. "Subsampling Intervals in Autoregressive Models with Linear Time Trend," Econometrica, Econometric Society, vol. 69(5), pages 1283-1314, September.
    3. Hinich , Melvin J. & Rothman, Philip, 1998. "Frequency-Domain Test Of Time Reversibility," Macroeconomic Dynamics, Cambridge University Press, vol. 2(01), pages 72-88, March.
    4. Darolles, Serge & Florens, Jean-Pierre & Gourieroux, Christian, 2004. "Kernel-based nonlinear canonical analysis and time reversibility," Journal of Econometrics, Elsevier, vol. 119(2), pages 323-353, April.
    5. Chen, Yi-Ting & Chou, Ray Y. & Kuan, Chung-Ming, 2000. "Testing time reversibility without moment restrictions," Journal of Econometrics, Elsevier, vol. 95(1), pages 199-218, March.
    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. Marc Hallin & Claude Lefèvre & Madan Lal Puri, 1988. "On time-reversibility and the uniqueness of moving average representations for non-Gaussian stationary time series," ULB Institutional Repository 2013/2017, ULB -- Universite Libre de Bruxelles.
    8. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
    9. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    10. Shao, Qi-Man & Yu, Hao, 1993. "Bootstrapping the sample means for stationary mixing sequences," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 175-190, October.
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    Cited by:

    1. Beare, Brendan K. & Seo, Juwon, 2014. "Time Irreversible Copula-Based Markov Models," Econometric Theory, Cambridge University Press, vol. 30(05), pages 923-960, October.
    2. Zacharias Psaradakis & Marián Vávra, 2015. "A Quantile-based Test for Symmetry of Weakly Dependent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 587-598, July.
    3. Anastassia Baxevani & Krzysztof Podgórski & Jörg Wegener, 2014. "Sample Path Asymmetries in Non-Gaussian Random Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1102-1123, December.
    4. Sebastian Schweer & Christian H. Weiß, 2016. "Testing for Poisson arrivals in INAR(1) processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 503-524, September.

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