• backtesting
• econometrics
• Expected Shortfall
• financial econometrics
• garch
• risk measure
• time series
• Value at Risk
• volatility

The need of proper investment decisions and capital adeguacy led practictioners and researchers in developing different statistical model specifications in order to forecast reliable market risk measurments.
Focusing on Autoregressive Conditional Heteroskedasticity (ARCH) models as statistical tools for forecasting conditional volatility and associated risk measures, this thesis provides an application of the two-stage procedure from Angelidis et al. as a guide to risk managers in backtesting and selecting the appropriate model in forecasting Value At Risk and Expected Shortfall.
Based on closing prices of S&P 500 index from 2007 to 2019, combinations of four classical GARCH models and six different error distributions are considered in order to forecast 1500 one-step ahead Value at Risk, with confidence levels of 1% and 5%, and Expected Shortfall. In addition, in order to asses the impact of different number of past observations in forecasting, four type of forecasting windows are also considered and compared.