Truncated Maximum Likelihood, and Nonparametric Tail Analysis

We propose a new approach to tail analysis for data featuring high degrees of leptokurtosis. Heavy tails can typically be found in financial series, like stock returns or durations between trade arrivals. Our method of tail assessment consists in fitting selected pseudo-models to varying subsets of extreme observations in the sample. The shape of tails is revealed by the tail parameter function, formed by a sequence of truncated pseudo-maximum likelihood estimators.