Modelling Value-at-Risk and Expected Shortfall for a Small Capital Market: Do Fractionally Integrated Models and Regime Shifts Matter?

Abstract

In this study, we examine the relevance of the coexistence of structural change and long memory to model and forecast the volatility of Tunisian stock returns and to deliver a more accurate measure of risk along the lines of VaR and expected shortfall. To this end, we propose three time-series models that incorporate long-term dependence on the level and volatility of returns. In addition, we introduce structural change points using the iterated cumulative sums of squares (ICSS) and the modified ICSS algorithms, synonymous with stock market turbulence, into the conditional variance equations of the models studied. We choose a conditional innovation density function other than the normal distribution, that is, a Student distribution, to account for excess kurtosis. The empirical results show that the inclusion of structural breakpoints in the conditional variance equation and Dual LM provides better short- and long-term predictability. Within such a framework, the ICSS-ARFIMA-HYGARCH model with Student’s t distribution was able to account for the long-term dependence in the level and volatility of TUNINDEX index returns, excess kurtosis, and structural changes, delivering an accurate estimator of VaR and expected shortfall.