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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.

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  • Escanciano, J. Carlos, 2010. "Asymptotic Distribution-Free Diagnostic Tests For Heteroskedastic Time Series Models," Econometric Theory, Cambridge University Press, vol. 26(03), pages 744-773, June.
  • Handle: RePEc:cup:etheor:v:26:y:2010:i:03:p:744-773_99
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    1. repec:spr:testjl:v:27:y:2018:i:1:d:10.1007_s11749-016-0506-2 is not listed on IDEAS
    2. Perera, Indeewara & Koul, Hira L., 2017. "Fitting a two phase threshold multiplicative error model," Journal of Econometrics, Elsevier, vol. 197(2), pages 348-367.
    3. 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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