Evaluations of likelihood based surveillance of volatility

The volatility of asset returns are important in finance. Different likelihood based methods of statistical surveillance for detecting a change in the variance are evaluated. The differences are how the partial likelihood ratios are weighted. The full likelihood ratio, Shiryaev-Roberts, Shewhart and the CUSUM methods are derived in case of an independent and identically distributed Gaussian process. The behavior of the methods is studied both when there is no change and when the change occurs at different time points. The false alarms are controlled by the median run length. Differences and limiting equalities of the methods are shown. The performances when the process parameters for which the methods are optimized for differ from the true values of the parameters are evaluated. The methods are illustrated on a period of Standard and Poor’s 500 stock market index.

Introduction: Timely detection of an important change in stochastic processes is important in many areas. In finance, detecting changes in assets prices or returns are important for investment decisions and Shiryaev (2002) demonstrated that change-points might induce arbitrage opportunities. The surveillance of business cycles, treated in the special issue (no. 3/4 1993) of Journal of Forecasting, Andersson et al. (2004),Andersson et al. (2005) and Andersson et al. (2006) is another important application. In quality control (Wetherhill and Brown (1991)), we may aim at timely detecting contaminated products in a manufacturing process. In medicine it is important to detect e.g. intrauterine growth retardation (Petzold et al. (2003)) or an increased incidence of a disease (Sonesson and Bock (2003)). Different medical applications are described in the special issue (no. 3 1989) of Statistics in Medicine.

Author: David Bock

Source: Göteborg University

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