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

  • Esfandiar Maasoumi
  • Jeffrey Racine

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.

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Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 28 (2009)
Issue (Month): 1-3 ()
Pages: 246-261

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Handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:246-261
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  1. Jushan Bai & Serena Ng, 2001. "Tests for Skewness, Kurtosis, and Normality for Time Series Data," Boston College Working Papers in Economics 501, Boston College Department of Economics.
  2. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
  3. Robinson, P M, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 437-53, May.
  4. Bai, Jushan & Ng, Serena, 2001. "A consistent test for conditional symmetry in time series models," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 225-258, July.
  5. McQueen, Grant & Thorley, Steven, 1993. "Asymmetric business cycle turning points," Journal of Monetary Economics, Elsevier, vol. 31(3), pages 341-362, June.
  6. 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.
  7. 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.
  8. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
  9. 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.
  10. 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, 09.
  11. 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.
  12. 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.
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