Bootstrapowe prognozy zmienności stóp zwrotu na podstawie modelu GARCH
Bootstrap predictions of returns for GARCH processes

Summary/Abstract: It is well known that high frequency financial time series are characterized by having conditional heteroscedasticity. The GARCH class of models is a convenient way to describe the phenomena of stock returns and represent the dynamic evolution of conditional variance. However, in the area of finance risk management equally important is the prediction of volatility of returns. This paper proposes using a bootstrap procedure to construct the prediction distribution of levels and volatilities and obtain prediction intervals of time series generated by AR(1)-GARCH(1,1) processes. Bootstrap-based methods allow for obtaining prediction intervals without distributional assumptions on the sequence of innovations. The bootstrap prediction intervals and traditional asymptotic prediction intervals are compared and it is found that the bootstrap leads to the improved accuracy.

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