Ahlstedt, Monica
(1997)
Suomen Pankin keskustelualoitteita 7/1997
The study derives a theoretically and empirically founded procedure for volatility estimation and forecasting of daily financial return series for use in value-at-risk model frameworks.GARCH modelling is applied to account for time varying heteroskedastic conditional variances and covariances.Through univariate estimation, the historical conditional variance models are specified within a group of twelve markka-denominated exchange rates, a group of thirteen short-term interest rates, the long-term interest rate and Finland's general stock market index.Within these groups, the method of principal components is used to detect common short-term factors driving the high frequency stochastic processes.Spectral analysis is applied to identify the length and regularity in the cyclical behaviour of the estimated conditional variances and their principal components.Since there turned out to be a great similarity in the univariate estimation results within groups of rates, GARCH estimation on pooled data was performed to force the rates within groups into the same model.The estimated models on pooled data were found to be integrated in variance with closely similar parameter values for both exchange rates and interest rates. Since a general multivariate framework is not possible to apply to the amount of series in this study due to the huge number of parameters to be identified, the covariances were calculated in two step-wise ways from the univariately estimated variances.First, assuming dependence between the autocorrelation structure of the conditional variances and covariances, univariately estimated parameters of the conditional variance models were used in identifying the pairs of conditional covariances.Second, assuming constant correlations, conditional covariances were estimated using joint information on the correlation coefficients of the GARCH standardized residuals and the univariate conditional variances. The first method is only applicable in estimating covariances within groups, the second is also applied in estimating the covariances between groups. Although the magnitude or direction of the expected changes in rates cannot be forecast, the estimated GARCH structure makes it possible to forecast the expected future variances.By developing the parameter structure estimated on pooled data, a theoretically and empirically founded procedure is suggested to replace the usual ad hoc decision process of selecting the sample period and the weight structure for estimating variances and covariances. Keywords: Time-dependent volatility, GARCH estimation, value-at-risk models