Kurtosis-based projection pursuit for outlier detection in financial time series

Outlier detection in financial time series is made difficult by serial dependence, volatility clustering and heavy tails. Projections achieving maximal kurtosis proved to be useful for outlier detection in multivariate datasets but their widespread application has been hampered by computational and inferential difficulties. This paper addresses both problems within the framework of univariate and multivariate financial time series. Computation of projections with maximal kurtoses in univariate financial time series is simplified to a eigenvalue problem. Projections with maximal kurtoses in multivariate financial time series best separate outliers from the bulk of the data, under a finite mixture model. The paper also addresses kurtosis optimization within the framework of portfolio selection. Practical relevance of these theoretical results is illustrated with univariate and multivariate time series from several financial markets. Empirical results also suggest that projections removing excess kurtosis could transform a univariate financial time series to a time series very similar to a Gaussian process, while the effect of outliers might be alleviated by projections achieving minimal kurtosis.