Sequential Monitoring for Changes in Dynamic Semiparametric Risk Models

We propose a sequential monitoring scheme to detect changes in dynamic semiparametric risk models that capture Value–at–Risk (VaR) and Expected Shortfall (ES) jointly. The monitoring scheme is based on a gradient–based detector and a boundary function, and a change is detected when the detector crosses the boundary function. We derive the asymptotic limit of the stopping time of detection under the null hypothesis of no change. Monte Carlo simulations show that the proposed test has reasonable size control under the null hypothesis and high power under alternative hypotheses of various change point scenarios in finite samples. Empirical applications based on the S&P 500 index and the GBP/EUR exchange rate illustrate that our proposed test is able to detect change points in real–time.