Two-sided exponential–geometric distribution: inference and volatility modeling

Abstract

In this paper, two-sided exponential–geometric (TSEG) distribution is proposed and its statistical properties are studied comprehensively. The proposed distribution is applied to the GJR-GARCH model to introduce a new conditional model in forecasting Value-at-Risk (VaR). Nikkei-225 and BIST-100 indexes are analyzed to demonstrate the VaR forecasting performance of GJR-GARCH-TSEG model against the GJR-GARCH models defined under normal, Student-t, skew-T and generalized error innovation distributions. The backtesting methodology is used to evaluate the out-of-sample performance of VaR models. Empirical findings show that GJR-GARCH-TSEG model produces more accurate VaR forecasts than other competitive models.