Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models
In this article we study a general class of goodness-of-fit tests for the conditional mean of a linear or nonlinear time series model. Among the properties of the proposed tests are that they are suitable when the conditioning set is infinite-dimensional; are consistent against a broad class of alternatives including Pitman's local alternatives converging at the parametric rate; and do not need to choose a lag order depending on the sample size or to smooth the data. It turns out that the asymptotic null distributions of the tests depend on the data generating process, so a new bootstrap procedure is proposed and theoretically justified. The proposed bootstrap tests are robust to higher order dependence, in particular to conditional heteroskedasticity of unknown form. A simulation study compares the finite sample performance of the proposed and competing tests and shows that our tests can play a valuable role in time series modeling. Finally, an application to an economic price series highlights the merits of our approach.
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Volume (Year): 101 (2006)
Issue (Month): (June)
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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Efstathios Paparoditis, 2000. "Spectral Density Based Goodness-of-Fit Tests for Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 143-176.
- Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
- Juan Carlos Escanciano, 2004. "Model Checks Using Residual Marked Empirical Processes," Faculty Working Papers 13/04, School of Economics and Business Administration, University of Navarra.
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- Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February.
- Pena D. & Rodriguez J., 2002. "A Powerful Portmanteau Test of Lack of Fit for Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 601-610, June.
- Escanciano, J. Carlos & Velasco, Carlos, 2006.
"Generalized spectral tests for the martingale difference hypothesis,"
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- J. Carlos Escanciano & Carlos Velasco, 2003. "Generalized Spectral Tests For The Martingale Difference Hypothesis," Statistics and Econometrics Working Papers ws035212, Universidad Carlos III, Departamento de Estadística y Econometría.
- Hong, Yongmiao & Lee, Tae-Hwy, 2003. "Diagnostic Checking For The Adequacy Of Nonlinear Time Series Models," Econometric Theory, Cambridge University Press, vol. 19(06), pages 1065-1121, December.
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