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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.

Suggested Citation

  • Marcelo Fernandes & Breno Neri, 2010. "Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 276-306.
    • Handle: RePEc:taf:emetrv:v:29:y:2010:i:3:p:276-306
    DOI: 10.1080/07474930903451557
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    2. George Kapetanios, 2007. "A Test for Serial Dependence Using Neural Networks," Working Papers 609, Queen Mary University of London, School of Economics and Finance.
    3. 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).
    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.
    5. Atanu Biswas & Maria Carmen Pardo & Apratim Guha, 2014. "Auto-association measures for stationary time series of categorical data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 487-514, September.
    6. Paulo Ferreira & Andreia Dion�sio, 2014. "Revisiting serial dependence in the stock markets of the G7 countries, Portugal, Spain and Greece," Applied Financial Economics, Taylor & Francis Journals, vol. 24(5), pages 319-331, March.
    7. Luca Bagnato & Lucio De Capitani & Antonio Punzo, 2014. "Testing Serial Independence via Density-Based Measures of Divergence," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 627-641, September.
    8. George Kapetanios, 2007. "A Test for Serial Dependence Using Neural Networks," Working Papers 609, Queen Mary University of London, School of Economics and Finance.

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