A study on window-size selection for threshold and bootstrap value-at-risk models

Anri Smith and Chun-Kai Huang

Abstract

This paper investigates the effects of window-size selection on various models for value-at-risk (VaR) forecasting using high-performance computing. Subsequently, automated procedures using change-point analysis for optimal window-size selection are proposed. In particular, stationary bootstrapping and the peaks-over-threshold method are utilized for a rolling daily VaR estimation and are contrasted with the classical conditional Gaussian model. It is evidenced that change-point procedures can, on average, result in more adequate risk predictions than a predetermined, fixed window size. The data sets analyzed include indexes across five continents, ie, the Dow Jones Industrial Average Index (DJI), the Financial Times Stock Exchange 100 Index (UKX), the Nikkei Top 225 Index (NKY), the Johannesburg Stock Exchange Top 40 Index (JSE Top 40), the Ibovespa Brazil Sao Paulo Stock Exchange All Index (IBOV) and the Bombay Stock Exchange Top 500 Index (BSE 500).