Kurtosis Maximization for Outlier Detection in GARCH Models

Abstract

Outlier detection in financial time series is made difficult by serial dependence, volatility clustering and heavy tails. We address these problems by filtering financial data with projections achieving maximal kurtosis. This method, also known as kurtosis-based projection pursuit, proved to be useful for outlier detection but its use has been hampered by computational difficulties. This paper shows that in GARCH models projections maximizing kurtosis admit a simple analytical representation which greatly eases their computation. The method is illustrated with a simple GARCH model.