Estimation of time dependent volatility via local change point analysis
- Mercurio, Danilo
- Spokoiny, Vladimir
2010 Mathematics Subject Classification
- 62M10 62P20
- volatility model, adaptive estimation, local homogeneity, change point
This paper offers a new procedure for estimation and forecasting of the volatility of financial time series. The approach is based on the assumption of local homogeneity: for every time point there exists an interval of time homogeneity in which the volatility parameter can be well approximated by a constant. The procedure recovers this interval from the data using the local change point analysis. Afterwards the estimate of the volatility can be simply obtained by local averaging. We investigate the performance of the procedure both from the theoretical point of view and through Monte Carlo simulations. Then the new procedure is applied to some data sets and a comparison with the LAVE procedure from Mercurio and Spokoiny (2004) and with a standard GARCH model is also provided. Finally we apply the new method for the The numerical results demonstrate a very reasonable performance of the new method.