A Comparison of GARCH-class Models and MIDAS Regression with Applications in Volatility Prediction and Value at Risk Estimation

Abstract: We use GARCH(1,1), EGARCH and MIDAS regression to forecast weekly and monthly conditional variance of the OMXS30 equity index and USD/SEK exchange rate. Forecasts are compared with realized volatility and accuracy is evaluated using a Quasi-likelihood loss function and Diebold Mariano test. We estimate normal and t-distributed Value at Risk using forecasted conditional variances and evaluate these estimates using Likelihood Ratio tests for unconditional coverage and temporal independence. We show that MIDAS regression outperforms both GARCH-class models in forecast accuracy, while the difference between GARCH(1,1) and EGARCH varies between data and frequency. Findings suggest that GARCH-class models underestimate conditional variance and react slowly to shocks, producing temporally dependent Value at Risk exceptions for some data. The superiority of MIDAS regression in the variance forecasting problem has implications for option pricing and risk management in the financial sector.