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Entropy Testing for Nonlinearity in Time Series

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  • Simone Giannerini
  • Eefandiar Maasoumi
  • Estela Bee Dagum

Abstract

We propose a test for identification of nonlinear serial dependence in time series against the 15 general "null" of linearity, in contrast to the more widely examined null of "independence." The approach is based on a combination of an entropy dependence metric, possessing many desirable properties and used as a test statistic, together with i) a suitable extension of surrogate data methods, a class of Monte Carlo distribution-free tests for nonlinearity; and ii) the use of a smoothed sieve bootstrap scheme. We show how the tests can be employed to detect the lags at which a 20 significant nonlinear relationship is expected in the same fashion as the autocorrelation function is used for linear models. We prove the asymptotic validity of the procedures proposed and of the corresponding inferences. The small sample size performance of the tests is assessed through a simulation study. Applications to real data sets of different kinds are also presented.

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Paper provided by Department of Economics, Emory University (Atlanta) in its series Emory Economics with number 1307.

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Date of creation: Aug 2013
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Handle: RePEc:emo:wp2003:1307

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  1. Fernandes, Marcelo, 2001. "Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes," Economics Working Papers (Ensaios Economicos da EPGE) 413, FGV/EPGE Escola Brasileira de Economia e Finan├žas, Getulio Vargas Foundation (Brazil).
  2. 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.
  3. Esfandiar Maasoumi & Jeffrey S. Racine, 2008. "A Robust Entropy-Based Test of Asymmetry for Discrete and Continuous Processes," Emory Economics 0806, Department of Economics, Emory University (Atlanta).
  4. 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.
  5. Robinson, P M, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 437-53, May.
  6. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
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