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Asymptotic Distribution-Free Diagnostic Tests For Heteroskedastic Time Series Models

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  • Escanciano, J. Carlos

Abstract

This article investigates model checks for a class of possibly nonlinear heteroskedastic time series models, including but not restricted to ARMA-GARCH models. We propose omnibus tests based on functionals of certain weighted standardized residual empirical processes. The new tests are asymptotically distribution-free, suitable when the conditioning set is infinite-dimensional, and consistent against a class of Pitman’s local alternatives converging at the parametric rate n−1/2, with n the sample size. A Monte Carlo study shows that the simulated level of the proposed tests is close to the asymptotic level already for moderate sample sizes and that tests have a satisfactory power performance. Finally, we illustrate our methodology with an application to the well-known S&P 500 daily stock index. The paper also contains an asymptotic uniform expansion for weighted residual empirical processes when initial conditions are considered, a result of independent interest.

Suggested Citation

  • Escanciano, J. Carlos, 2010. "Asymptotic Distribution-Free Diagnostic Tests For Heteroskedastic Time Series Models," Econometric Theory, Cambridge University Press, vol. 26(3), pages 744-773, June.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:03:p:744-773_99
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    References listed on IDEAS

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    1. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    2. Carlos Escanciano, J., 2008. "Joint and marginal specification tests for conditional mean and variance models," Journal of Econometrics, Elsevier, vol. 143(1), pages 74-87, March.
    3. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 134(1), pages 151-185, September.
    4. Escanciano, J. Carlos, 2006. "Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 531-541, June.
    5. 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.
    6. Bera, Anil K & Higgins, Matthew L, 1997. "ARCH and Bilinearity as Competing Models for Nonlinear Dependence," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 43-50, January.
    7. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(5), pages 793-813, December.
    8. Hong, Yongmiao & Lee, Tae-Hwy, 2003. "Diagnostic Checking For The Adequacy Of Nonlinear Time Series Models," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1065-1121, December.
    9. Delgado, Miguel A. & Carlos Escanciano, J., 2007. "Nonparametric tests for conditional symmetry in dynamic models," Journal of Econometrics, Elsevier, vol. 141(2), pages 652-682, December.
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    Cited by:

    1. Hafner, C. M. & Linton, O. B. & Wang, L., 2024. "The Effect of Stock Splits on Liquidity in a Dynamic Model," Cambridge Working Papers in Economics 2410, Faculty of Economics, University of Cambridge.
    2. Perera, Indeewara & Silvapulle, Mervyn J., 2023. "Bootstrap specification tests for dynamic conditional distribution models," Journal of Econometrics, Elsevier, vol. 235(2), pages 949-971.
    3. Hafner, C. M. & Linton, O. B. & Wang, L., 2024. "The Effect of Stock Splits on Liquidity in a Dynamic Model," Janeway Institute Working Papers 2404, Faculty of Economics, University of Cambridge.
    4. Hafner, Christian & Linton, Oliver & Wang, Linqi, 2024. "The effect of stock splits on liquidity in a dynamic model," LIDAM Discussion Papers ISBA 2024007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Giuseppe Cavaliere & Indeewara Perera & Anders Rahbek, 2021. "Specification tests for GARCH processes," Discussion Papers 21-06, University of Copenhagen. Department of Economics.
    6. Christian Francq & Olivier Wintenberger & Jean-Michel Zakoïan, 2018. "Goodness-of-fit tests for Log-GARCH and EGARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 27-51, March.
    7. Alejandra Cabaña & Enrique M. Cabaña & Marco Scavino, 2012. "Weak Convergence of Marked Empirical Processes for Focused Inference on AR(p) vs AR(p + 1) Stationary Time Series," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 793-810, September.
    8. Anne Leucht & Jens-Peter Kreiss & Michael H. Neumann, 2015. "A Model Specification Test For GARCH(1,1) Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1167-1193, December.
    9. Perera, Indeewara & Koul, Hira L., 2017. "Fitting a two phase threshold multiplicative error model," Journal of Econometrics, Elsevier, vol. 197(2), pages 348-367.

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