Forecasting high and low of financial time series by particle filters and Kalman filters

Abstract

The analysis of financial time series is very useful in the economic world. This paper deals with a data-driven empirical analysis of financial time series. In this paper we present a forecasting method of the first stopping times, when the prices cross for the first time a "high" or "low" threshold defined by the trader, based on an empirical functional analysis of the past "tick data" of the series, without resampling. An originality of this method is that it does not use a theoretical financial model but a non-parametric space state representation with non-linear RBF neural networks. Modelling and forecasting are made by Particles systems and Kalman filters. This method can be applied to any forecasting problem of stopping time, but is particularly suited for data showing nonlinear dependencies and observed at irregularly and randomly spaced times like financial time series of «tick data» do. The method is applied to the forecasting of stopping times of "high" and "low" of financial time series in order to be useful for speculator