Chapter 35 - A Stable Cointegrated Var Model for Credit Returns with Time-Varying Volatility

Abstract

This chapter presents a stable cointegrated vector-autoregressive (VAR) model for credit returns with time-varying volatility. A framework is set up based on cointegrated vector-autoregression. It is assumed the variables of the model to follow a stable law as they exhibit peakedness and heavy-tailedness. For the residuals, time-varying volatilities are observed. While dealing with Value-at-Risk (VaR) applications, the forecast of conditional volatility and covariance is crucial. The multivariate constant correlation-Generalized Autoregressive Conditional Heteroscedasticity (CC-GARCH) bears the restriction of constant correlations. The extension of the univariate to the multivariate case is straightforward. It is assumed as a variance-covariance matrix following a GARCH process. The Mean-Squared Error (MSE) is a pure statistical loss function that can be applied to an in-sample volatility forecasting and an out-of-sample volatility forecasting. To evaluate the accuracy of value-at-risk measures, a test of the unconditional coverage is applied. The fitted parameters of the multivariate volatility models for the five residuals are also presented in the chapter.