The paper proposes sequential procedures for on-line monitoring volatility forecast. We are interested in a model which provides a proper short-term forecast for the asset returns variance. The variance is an unobservable process. It can be measured on high-frequency data by the realized volatility (RV) (Andersen and Bollerslev, 1998), the bipower variation (BV) (Barndorff-Nielsen and Shephard, 2004), or others approaches. If there is no jump component in the price equation, the RV is a consistent measure of the integrated (true) volatility (IV), otherwise the BV should be preferred due to its robustness against jumps. In case where the market microstructure noise is assumed to be a time series the staggered BV can be used. We propose to model the volatility process with a linear state space representation. The observation equation describes relation between a volatility measure and the IV. The state equation assumes that the IV follows an AR(1) process.
The model is useful for a short-term forecasting and does not allow any structural changes. For this reason it is required to check the validity of the model at each new time point. Control charts from statistical process control are suitable rules for this purpose (Montgomery, 2005). In the paper we provide the distribution of forecasting errors. The control charts are constructed on the forecasting errors. A signal of a control chart indicates on a possibility that the initial assumptions concerning the process of interest are no longer satisfied. We distinguish between signals caused by jumps in the price equation and signals caused by structural changes. The jump component is detected by the tests of Barndorff-Nielsen and Shephard (2004).
First task of the simulation study is to investigate which changes in the model parameters cause the largest forecasting losses. Second task is to analyze the ability of the considered control charts to detect these changes. We investigate the Shewhart control chart and three CUSUM-type control charts. In the empirical study our approach is illustrated on four U.S. stocks. The state space representation fits the data for all stocks in the in-sample period. The obtained signals of the control charts and the detected jumps occur usually on different days. The control charts reject clearly the model for one stock. The publically available information confirms this result. Therefore it is concluded that the signals point on structural changes in the model.
Andersen, T. G. and Bollerslev, T. (1998). Answering the skeptics: standard volatility models do provide accurate forecasts, International Economic Review 39: 885-905.
Barndorff-Nielsen, O. E. and Shephard, N. (2004). Power and bipower variation with stochastic volatility and jumps, Journal of Financial Econometrics 2: 1-37.
Montgomery, D. C. (2005). Introduction to Statistical Quality Control, 5th ed., Wiley: New York.
Keywords: Control charts; Integrated volatility; Realized volatility; State space model
Biography: Since October 2008 I am a research assistant at the Department of Statistics in European University Viadrina, Frankfurt (Oder), Germany. In June 2010 I have got the Ph.D. in Economics. My research interests are statistical process control, its application to multidimensional problems, for example for monitoring the optimal portfolio weights. I deal also with high-frequency data.