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Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models

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  • Escanciano, J. Carlos

Abstract

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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Suggested Citation

  • 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.
  • Handle: RePEc:bes:jnlasa:v:101:y:2006:p:531-541
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    References listed on IDEAS

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    1. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
    2. Brock, W.A. & Dechert, W.D. & LeBaron, B. & Scheinkman, J.A., 1995. "A Test for Independence Based on the Correlation Dimension," Working papers 9520, Wisconsin Madison - Social Systems.
    3. 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.
    4. 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.
    5. 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.
    6. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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