Non-parametric estimation of copula parameters: testing for time-varying correlation

The correlation structure of financial assets is a key input with regard to portfolio and risk management. In this paper, we propose a non-parametric estimation method for the time-varying copula parameter. This is achieved in two steps: first, displaying the marginal distributions of financial asset returns by applying the empirical distribution function; second, by implementing the local likelihood method to estimate the copula parameters. The method for obtaining the optimal bandwidth through a maximum pseudo likelihood function and a statistical test on whether the copula parameter is time-varying are also introduced. A simulation study is conducted to show that our method is superior to its contender. Finally, we verify the proposed estimation methodology and time-varying statistical test by analysing the dynamic linkages between the Shanghai, Shenzhen and Hong Kong stock markets.