Empirical analysis of ARMA-GARCH models in market risk estimation on high-frequency US data

In this paper, we examine the S&P 500 index log-returns on short intraday time scales with three different ARMA-GARCH models. In order to forecast market risk, we describe the innovation process with tempered stable distributions which we compare to commonly used methods in financial modeling. Value-at-risk backtests are provided where we find that models based on the tempered stable innovation assumption significantly outperform traditional models in forecasting risk on short time-scales. In addition to value-at-risk, the idiosyncratic differences in average value-at-risk are compared between the models.