Forecasting Value-at-Risk with Novel Wavelet Based Garch-EVT Model

In this study, wavelet based GARCH-Extreme Value Theory (EVT) is proposed to model financial return series to forecast daily value-at-risk. Wavelets based GARCH-EVT is hybrid model combining the wavelet analysis and EVT. Proposed model contains three stages. In first stage, return series is decomposed into wavelet series and approximation series by applying the maximal overlap discrete wavelet transform. Second stage, detrended return series and approximation series are obtained by using wavelet series and scaling series. GARCH model is fitted to each obtained series to forecast daily volatility. Final stage, EVT is used to estimate quantile estimation of standardized residuals of GARCH model obtained for detrended return series and daily VaR value is forecasted by using volatility forecasts and quantile estimation. Daily VaR forecasting accuracy of proposed hybrid model is compared with the GARCH models specified under heavy-tailed distributions and GARCH-EVT model. Empirical findings show that wavelet based GARCH-EVT model is outperformed at high quantiles according to backtesting results.