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Goodness-Of-Fit Test For Nonlinear Time Series Models

Author

Listed:
  • NGAI SZE HAN

    (Hong Kong Examinations and Assessment Authority, Hong Kong)

  • SHIQING LING

    (#x2020;Hong Kong University of Science and Technology, Department of Mathematics, Clear Water Bay, Hong Kong)

Abstract

Many time series models have been used extensively in modeling economic and financial data. However, it is difficult to determine the functional forms of the conditional mean and conditional variance in these models. In this paper, a test statistic based on the squared conditional residuals is proposed for testing these functional forms, and the asymptotic distribution of the test statistic is obtained. The test statistic is applicable not only to the family of GARCH models but also to other nonlinear time series models. Simulation results show that the proposed tests are powerful and have reasonable sizes. Two real examples are also given to illustrate our theory.

Suggested Citation

  • Ngai Sze Han & Shiqing Ling, 2017. "Goodness-Of-Fit Test For Nonlinear Time Series Models," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 1-21, June.
  • Handle: RePEc:wsi:afexxx:v:12:y:2017:i:02:n:s2010495217500063
    DOI: 10.1142/S2010495217500063
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    References listed on IDEAS

    as
    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
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    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-158, February.
    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. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
    8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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