Nonparametric kernel estimation for local tail-event correlation

Abstract

We propose a local tail-event correlation which measures local tail dependence between a pair of time series. The local tail-event correlation is the tail correlation locally estimated by a nonparametric kernel method in order to grasp change in tail dependence over time. We establish asymptotic normality of the local tail-event correlation which enables us to develop statistical inferences such as confidence interval, homogeneity test and predictability test at specific time points. A Monte Carlo simulation demonstrates finite sample validity of the proposed statistical inferences via reasonable coverage, size and power performances. The local tail-event correlation is applied to financial stock returns. The predictability analysis tells us that 10% tail correlations between yesterday log-return of major companies (Apple, Amazon, United Health Group) and today log-return of a financial system (US S&P 500 index) are statistically significant, changing over time, but the tail correlations at the median level do not change. The tail dependence analysis finds that 10% left-tail correlations of the log-returns of financial system (US S&P 500 index) and the financial institution (J.P Morgan, Bank of America or Wells Fargo & Co) are significantly stronger during the global financial crisis than before the crisis, but the tail correlations at median level do not show significant change during that period.