Forecasting Time-varying Value--at--Risk and Expected Shortfall Dependence: A Markov-switching Generalized Autoregressive Score Copula Approach

Abstract

The importance of accurately forecasting extreme financial losses and their effects on the institutions involved in a given financial market has been highlighted by recent financial catastrophes. The flexibility with which econometric models can take into account the highly non-linear and asymmetric dependence in financial returns is a critical component of their capacity to forecast extreme events. Therefore, this study aims to forecast time-varying Value-at-Risk and expected shortfall dependence as a predictive density-based regime changes over time. To achieve this, a non-stationary Markov-switching generalized Autoregressive score model nested with copula is estimated using expectation–maximization (EM) algorithm. Extending this non-stationary model is quite challenging, as it requires specifications not only on how the usual parameters change over time but also those with mass distribution components. Dynamics of the estimated autoregressive score allowed the copula parameters to respond rapidly to time-varying key systemic parameters and risk. This is because regime changes are allowed to oscillated between high and low regimes. This is a clear indication of a regime shift in the parameters of an estimated model. Using the minimum score combining, six extreme value distributions are combined to the estimated MS(2)-GAS(1)-copula model and assessed the performance of each combined model 5 days and 30 days forecasting of value-at-risk and expected shortfall. The results of the forecasting performance indicated that the MS(2)-GAS(1)-GPD is the best model to model and forecast Value-at-risk and expected shortfall for the Botswana stock market. This is a promising technique for stochastic modeling of time-varying Value-at-Risk and Expected Shortfall. In addition, a foundation is provided for future researchers to conduct studies on emerging markets. These results are also important for risk managers and investors.