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Assessing Time‐Reversibility Under Minimal Assumptions

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  • Zacharias Psaradakis

Abstract

. 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.

Suggested Citation

  • 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
    DOI: 10.1111/j.1467-9892.2008.00587.x
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    References listed on IDEAS

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    7. Chen Yi-Ting, 2003. "Testing Serial Independence against Time Irreversibility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(3), pages 1-30, October.
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    1. Beare, Brendan K. & Seo, Juwon, 2014. "Time Irreversible Copula-Based Markov Models," Econometric Theory, Cambridge University Press, vol. 30(5), pages 923-960, October.
    2. Amit Shelef & Edna Schechtman, 2019. "A Gini-based time series analysis and test for reversibility," Statistical Papers, Springer, vol. 60(3), pages 687-716, June.
    3. Shibin Zhang, 2023. "A copula spectral test for pairwise time reversibility," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 705-729, October.
    4. 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.
    5. 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.
    6. 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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