GARCH models for daily stock returns: Impact of estimation frequency on Value-at-Risk and Expected Shortfall forecasts

- The impact of the estimation frequency of commonly used GARCH models is analyzed.
- VaR and ES forecasts are computed for different models and frequencies.
- The false discovery rate approach is used to correct for multiple testing bias (more than 1200 time series).

We analyze the impact of the estimation frequency-updating parameter estimates on a daily, weekly, monthly or quarterly basis-for commonly used GARCH models in a large-scale study, using more than twelve years (2000-2012) of daily returns for constituents of the S&P 500 index. We assess the implication for one-day ahead 95% and 99% Value-at-Risk (VaR) forecasts with the test for correct conditional coverage of Christoffersen (1998) and for Expected Shortfall (ES) forecasts with the block-bootstrap test of ES violations of Jalal and Rockinger (2008). Using the false discovery rate methodology of Storey (2002) to estimate the percentage of stocks for which the model yields correct VaR and ES forecasts, we conclude that there is no difference in performance between updating the parameter estimates of the GARCH equation at a daily or weekly frequency, whereas monthly or even quarterly updates are only marginally outperformed.