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A Robust Entropy-Based Test of Asymmetry for Discrete and Continuous Processes

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  • Esfandiar Maasoumi
  • Jeffrey Racine

Abstract

We consider a metric entropy capable of detecting deviations from symmetry that is suitable for both discrete and continuous processes. A test statistic is constructed from an integrated normed difference between nonparametric estimates of two density functions. The null distribution (symmetry) is obtained by resampling from an artificially lengthened series constructed from a rotation of the original series about its mean (median, mode). Simulations demonstrate that the test has correct size and good power in the direction of interesting alternatives, while applications to updated Nelson and Plosser (1982) data demonstrate its potential power gains relative to existing tests.

Suggested Citation

  • Esfandiar Maasoumi & Jeffrey Racine, 2009. "A Robust Entropy-Based Test of Asymmetry for Discrete and Continuous Processes," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 246-261.
  • Handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:246-261
    DOI: 10.1080/07474930802388066
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    1. Belaire-Franch Jorge & Peiro Amado, 2003. "Conditional and Unconditional Asymmetry in U.S. Macroeconomic Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(1), pages 1-19, April.
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    5. Gamini Premaratne, 2005. "A Test for Symmetry with Leptokurtic Financial Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(2), pages 169-187.
    6. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
    7. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    8. Dagum, Estela Bee & Giannerini, Simone, 2006. "A critical investigation on detrending procedures for non-linear processes," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 175-191, March.
    9. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    10. P. M. Robinson, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 437-453.
    11. C. W. Granger & E. Maasoumi & J. Racine, 2004. "A Dependence Metric for Possibly Nonlinear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 649-669, September.
    12. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
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    Cited by:

    1. David E. Allen & Michael McAleer & Robert Powell & Abhay K. Singh, 2013. "A Non-Parametric and Entropy Based Analysis of the Relationship between the VIX and S&P 500," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 6(1), pages 1-25, October.
    2. Renée Fry-McKibbin & Cody Yu-Ling Hsiao & Vance L. Martin, 2018. "Measuring financial interdependence in asset returns with an application to euro zone equities," CAMA Working Papers 2018-05, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    3. Simone Giannerini & Eefandiar Maasoumi & Estela Bee Dagum, 2013. "Entropy Testing for Nonlinearity in Time Series," Emory Economics 1307, Department of Economics, Emory University (Atlanta).
    4. Rafael Salas & Juan Rodríguez, 2013. "Popular support for social evaluation functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 985-1014, April.
    5. Fang, Ying & Li, Qi & Wu, Ximing & Zhang, Daiqiang, 2015. "A data-driven smooth test of symmetry," Journal of Econometrics, Elsevier, vol. 188(2), pages 490-501.
    6. Narayan, Paresh Kumar & Popp, Stephan, 2009. "Can the electricity market be characterised by asymmetric behaviour?," Energy Policy, Elsevier, vol. 37(11), pages 4364-4372, November.
    7. Yoon, Gawon, 2010. "Do real exchange rates really follow threshold autoregressive or exponential smooth transition autoregressive models?," Economic Modelling, Elsevier, vol. 27(2), pages 605-612, March.

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    Keywords

    Entropy; Kernel; Metric; Nonparametric; Symmetry; Time series;

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