Skip to main content
SpringerLink
Log in

A test of conditional heteroscedasticity in time series

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

A new test of conditional heteroscedasticity for time series is proposed. The new testing method is based on a goodness of fit type test statistics and a Cramer-von Mises type test statistic. The asymptotic properties of the new test statistic is establised. The results demonstrate that such a test is consistent.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Engle, R. F., Autoregressive conditional heteroscedasticity with estimates of the variance of U. inflation,Econometrika, 1980, 50: 987.

    Article  MathSciNet  Google Scholar 

  2. Bollerslev, T., Chou, R. Y., Kroner, F., ARCH modeling in finance,J. of Econometrics, 1992, 52: 5.

    Article  MATH  Google Scholar 

  3. Tong, H., Non-linear Time Series: A Dynamical System Approach, London; Oxford Univ. Press, 1990.

    MATH  Google Scholar 

  4. Engle, R. F., Hendry, D. F., Frumele, D., Small sample properties of ARCH estimators and tests,Canadian J.Ecrn., 1985, 18: 66.

    Article  Google Scholar 

  5. Li, W.K, Mak, T. K., On the squared residual autocorrelations in nonlinear time series with conditional heteroscedasticity,J. Time Series Anal., 1994, 15: 627.

    Article  MATH  MathSciNet  Google Scholar 

  6. Chen, M., An, H. Z., A Kolmogorov-Smirnov type test for conditional heteroscedasticity in time series,Statist. & Prob. Letters, 1997, 33: 321.

    Article  MATH  MathSciNet  Google Scholar 

  7. An, H. Z., Chen, M., Huang, F. C., The geometrical ergodicity and the existence of moments of a class nonlinear time series model,Statist. & Prob. Letters, 1997, 31: 213.

    Article  MATH  MathSciNet  Google Scholar 

  8. Hall, P., Heyde, C.C.,Martingale Limit Theory and Its Applications, New York: Academic Press, 1980.

    Google Scholar 

  9. An, H. Z., Chen, Z. G., Hannan, E. J., Autocorrelation, autoregression and autoregressive approximation,Ann. Statist., 1982, 10: 926.

    Article  MATH  MathSciNet  Google Scholar 

  10. Billingsly, P.,Convergence of Probability Measures, New York: John Wiley, 1968.

    Google Scholar 

  11. Huang, D. W., Convergence rate of sample autocorrelations and autocovariances for stationary time series,Scientia Sinica, Ser. A, 1988, 31: 406.

    MATH  Google Scholar 

  12. Horn, R. A., Johnson, C. R.,Matrix Analysis, London: Cambridge Univ. Press, 1985.

    MATH  Google Scholar 

  13. Chow, Y. S., Teicher, H.,Probability Theory, New York: Springer-Verlag, 1978.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Systems Science, Chinese Academy of Sciences, 100080, Beijing, China

    Min Chen

  2. Institute of Applied Mathematics, Chinese Academy of Sciences, 100080, Beijing, China

    Hongzhi An

Authors
  1. Min Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongzhi An
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Project supported by the National Natural Science Foundation of China (Grant No. 19231050) and Postdoctoral Fund of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, M., An, H. A test of conditional heteroscedasticity in time series. Sci. China Ser. A-Math. 42, 26–37 (1999). https://doi.org/10.1007/BF02872047

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02872047

Keywords

Search

Navigation