Confidence Intervals for the Autocorrelations of the Squares of GARCH Sequences

  • Piotr Kokoszka
  • Gilles Teyssière
  • Aonan Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3039)


We compare three methods of constructing confidence intervals for sample autocorrelations of squared returns modeled by models from the GARCH family. We compare the residual bootstrap, block bootstrap and subsampling methods. The residual bootstrap based on the standard GARCH(1,1) model is seen to perform best.


Coverage Probability GARCH Model Series Length Solid Horizontal Line Block Bootstrap 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bühlmann, P.: Bootstrap for time series. Statistical Science 17, 52–72 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Engle, R.F.: Discussion: stock market volatility and the crash of 87. Review of Financial Studies 3, 103–106 (1990)Google Scholar
  3. 3.
    Glosten, L.R., Jagannathan, R., Runkle, D.: On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance 48, 1779–1801 (1993)CrossRefGoogle Scholar
  4. 4.
    He, C., Teräsvirta, T.: Properties of moments of a family of GARCH processes. Journal of Econometrics 92, 173–192 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Künsch, H.: The jackknife and the bootstrap for general stationary observations. The Annals of Statistics 17, 1217–1241 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Mikosch, T., Stărică, C.: Limit theory for the sample autocorrelations and extremes of a GARCH(1,1) process. The Annals of Statistics 28, 1427–1451 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Politis, D.N., Romano, J.P., Wolf, M.: Subsampling. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  8. 8.
    Politis, D.N., Romano, J.P., Wolf, M.: Inference for autocorrelations in the possible presence of a unit root. Journal of Time series Analysis (to appear)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Piotr Kokoszka
    • 1
  • Gilles Teyssière
    • 2
  • Aonan Zhang
    • 3
  1. 1.Mathematics and StatisticsUtah State UniversityLoganUSA
  2. 2.NBG Bank (Paris) & ASEF 
  3. 3.Mathematics and StatisticsUtah State University 

Personalised recommendations