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Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes

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  • Marcelo Fernandes
  • Breno Neri

Abstract

This article develops nonparametric tests of independence between two stochastic processes satisfying β-mixing conditions. The testing strategy boils down to gauging the closeness between the joint and the product of the marginal stationary densities. For that purpose, we take advantage of a generalized entropic measure so as to build a whole family of nonparametric tests of independence. We derive asymptotic normality and local power using the functional delta method for kernels. As a corollary, we also develop a class of entropy-based tests for serial independence. The latter are nuisance parameter free, and hence also qualify for dynamic misspecification analyses. We then investigate the finite-sample properties of our serial independence tests through Monte Carlo simulations. They perform quite well, entailing more power against some nonlinear AR alternatives than two popular nonparametric serial-independence tests.

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Bibliographic Info

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

Volume (Year): 29 (2010)
Issue (Month): 3 ()
Pages: 276-306

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Handle: RePEc:taf:emetrv:v:29:y:2010:i:3:p:276-306

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Related research

Keywords: Independence; Misspecification testing; Nonparametric theory; Tsallis entropy;

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References

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  1. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
  2. Bruce Mizrach, 1995. "A Simple Nonparametric Test for Independence," Departmental Working Papers 199523, Rutgers University, Department of Economics.
  3. Peter C.B. Phillips, 1988. "Error Correction and Long Run Equilibrium in Continuous Time," Cowles Foundation Discussion Papers 882R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
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  5. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  6. Drost, F.C. & Werker, B.J.M., 1993. "A note on Robinson's test of independence," Discussion Paper 1993-15, Tilburg University, Center for Economic Research.
  7. Zheng, John Xu, 2000. "A Consistent Test Of Conditional Parametric Distributions," Econometric Theory, Cambridge University Press, vol. 16(05), pages 667-691, October.
  8. Robinson, P M, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 437-53, May.
  9. Gregory, Allan W & Sampson, Michael J, 1991. "Testing Long-Run Properties of Stationary Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 287-95, July.
  10. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  11. Marc Hallin & Madan L. Puri, 1992. "Rank tests for time-series analysis: a survey," ULB Institutional Repository 2013/2229, ULB -- Universite Libre de Bruxelles.
  12. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, 05.
  13. Marc Hallin & Jana Jureckova & Jan Picek & Toufik Zahaf, 1999. "Nonparametric tests of independence between two autoregressive series based on autoregression rank scores," ULB Institutional Repository 2013/2081, ULB -- Universite Libre de Bruxelles.
  14. Yanqin Fan & Oliver Linton, 1997. "Some Higher Order Theory for a Consistent Nonparametric Model Specification Test," Cowles Foundation Discussion Papers 1148, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. George Kapetanios, 2007. "A Test for Serial Dependence Using Neural Networks," Working Papers 609, Queen Mary, University of London, School of Economics and Finance.
  2. Paulo Ferreira, 2012. "Testing serial dependence in the stock markets of the G7 countries, Portugal, Spain and Greece," CEFAGE-UE Working Papers 2012_24, University of Evora, CEFAGE-UE (Portugal).
  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. Menezes, Rui & Dionísio, Andreia & Hassani, Hossein, 2012. "On the globalization of stock markets: An application of Vector Error Correction Model, Mutual Information and Singular Spectrum Analysis to the G7 countries," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(4), pages 369-384.

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