Semi Parametric Estimation of the Dependence Structure of Financial Time Series using Copulas

Abstract

Dependence of financial variables is a key concern for financial risk analysts and investors. With the increasing application of copula in finance, there is need to have robust and consistent estimators of copula parameters. Though the existing parametric and semi parametric estimators are robust, they capture static dependence between variables. There is documented evidence of time variation of the dependence between financial time series data. This thesis uses the moving window estimator to capture time varying dependence of financial time series data. The moving window estimation technique is formulated as an extension of the semi parametric copula based multivariate dynamical model to the changing values in the sub samples. Thus the moving window estimator inherits the consistency and asymptotic normality of the semi parametric estimator. The thesis applies the semi parametric and moving window copula estimation techniques to capture and test for dependence of the daily equity and foreign exchange returns data in Kenya. The multivariate dependence test reveals significant positive correlation between the Nairobi Securities Exchange 20-share index and the Kenya Shilling versus the United States dollar exchange rate. Amongst the parametric copula models fitted into the data, the t copula with 10 degrees of freedom is found to be the most appropriate for capturing the static dependence over the entire study period