Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Stationary Bootstrap Prediction Intervals for GARCH(p,q)

  • Hwang, Eunju (Institute of Mathematical Sciences and Department of Statistics, Ewha Womans University) ;
  • Shin, Dong Wan (Institute of Mathematical Sciences and Department of Statistics, Ewha Womans University)
  • Received : 2012.10.10
  • Accepted : 2012.12.22
  • Published : 2013.01.31
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Abstract

The stationary bootstrap of Politis and Romano (1994) is adopted to develop prediction intervals of returns and volatilities in a generalized autoregressive heteroskedastic (GARCH)(p, q) model. The stationary bootstrap method is applied to generate bootstrap observations of squared returns and residuals, through an ARMA representation of the GARCH model. The stationary bootstrap estimators of unknown parameters are defined and used to calculate the stationary bootstrap samples of volatilities. Estimates of future values of returns and volatilities in the GARCH process and the bootstrap prediction intervals are constructed based on the stationary bootstrap; in addition, asymptotic validities are also shown.

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References

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