A New multivariate nonlinear time series model for portfolio risk measurement: the threshold copula-based TAR approach

We propose a threshold copula-based nonlinear time series model for evaluating quantitative risk measures for financial portfolios with a flexible structure to incorporate nonlinearities in both univariate (component) time series and their dependent structure. We incorporate different dependent structures of asset returns over different market regimes, which are manifested in their price levels. We estimate the model parameters by a two-stage maximum likelihood method. Real financial data and appropriate statistical tests are used to illustrate the efficacy of the proposed model. Simulated results for sampling distribution of parameters estimates are given. Empirical results suggest that the proposed model leads to significant improvement of the accuracy of value-at-risk forecasts at the portfolio level.