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Testing Non-linearity Using a Modified Q Test

  • Marian Vavra

    (Department of Economics, Mathematics & Statistics, Birkbeck)

A new version of the Q test, based on generalized residual correlations (i.e. auto-correlations and cross-correlations), is developed in this paper. The Q test fixes two main shortcomings of the Mcleod and Li Q (MLQ) test often used in the literature: (i) the test is capable to capture some interesting non-linear models, for which the original MLQ test completely fails (e.g. a non-linear moving average model). Additionally, the Q test also significantly improves the power for some other non-linear models (e.g. a threshold moving average model), for which the original MLQ test does not work very well; (ii) the new Q test can be used for discrimination between simple and more complicated (non-linear/asymmetric) GARCH models as well.

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File URL: http://www.bbk.ac.uk/ems/research/wp/2012/PDFs/BWPEF1204.pdf
File Function: First version, 2012
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Paper provided by Birkbeck, Department of Economics, Mathematics & Statistics in its series Birkbeck Working Papers in Economics and Finance with number 1204.

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Date of creation: Mar 2012
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Handle: RePEc:bbk:bbkefp:1204
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  1. Runde, Ralf, 1997. "The asymptotic null distribution of the Box-Pierce Q-statistic for random variables with infinite variance an application to German stock returns," Journal of Econometrics, Elsevier, vol. 78(2), pages 205-216, June.
  2. Ana PĂ©rez & Esther Ruiz, 2003. "Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(3), pages 420-444.
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  4. Dennis Jansen & Casper de Vries, 1988. "On the frequency of large stock returns: putting booms and busts into perspective," Working Papers 1989-006, Federal Reserve Bank of St. Louis.
  5. Serena Ng & Pierre Perron, 2005. "A Note on the Selection of Time Series Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(1), pages 115-134, 02.
  6. Lobato I. N., 2001. "Testing That a Dependent Process Is Uncorrelated," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1066-1076, September.
  7. Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
  8. Horowitz, Joel L. & Lobato, I.N. & Nankervis, John C. & Savin, N.E., 2006. "Bootstrapping the Box-Pierce Q test: A robust test of uncorrelatedness," Journal of Econometrics, Elsevier, vol. 133(2), pages 841-862, August.
  9. Maravall, Agustin, 1983. "An Application of Nonlinear Time Series Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(1), pages 66-74, January.
  10. Lobato, I.N. & Nankervis, John C. & Savin, N.E., 2002. "Testing For Zero Autocorrelation In The Presence Of Statistical Dependence," Econometric Theory, Cambridge University Press, vol. 18(03), pages 730-743, June.
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