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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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    Cited by:

    1. K. Ghoudi & N. Laïb, 2025. "On joint testing of changes in conditional mean and variance functions of stationary and ergodic time series," Statistical Papers, Springer, vol. 66(5), pages 1-36, August.
    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, 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).
    4. Giuseppe Cavaliere & Indeewara Perera & Anders Rahbek, 2021. "Specification tests for GARCH processes," Discussion Papers 21-06, University of Copenhagen. Department of Economics.
    5. Tan, Falong & Guo, Xu & Zhu, Lixing, 2025. "Weighted residual empirical processes, martingale transformations, and model specification tests for regressions with diverging number of parameters," Journal of Econometrics, Elsevier, vol. 252(PA).
    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. Perera, Indeewara & Koul, Hira L., 2017. "Fitting a two phase threshold multiplicative error model," Journal of Econometrics, Elsevier, vol. 197(2), pages 348-367.
    8. Hafner, C. M. & Linton, O. B. & Wang, L., 2024. "The Permanent and Temporary Effects of Stock Splits on Liquidity in a Dynamic Semiparametric Model," Cambridge Working Papers in Economics 2410, Faculty of Economics, University of Cambridge.
    9. repec:cam:camjip:2404 is not listed on IDEAS
    10. 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.
    11. 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.

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