A Mean Reverting Stochastic Process (MRSP) using an AR(n) Model and a Kalman Filter for Generating Intravalues for the Daily DJIA Time Series

SUMMARY

This paper presents a model for generating intravalues of time-series. The model uses a mean reverting stochastic process (MRSP). The deterministic or mean part of the process is forecasted by an autoregressive of order n, AR(n), model. The unobservable AR(n) coefficients are calculated by a Kalman Filter using n time series observations. The stochastic part of the process is a Brownian motion multiplied by a volatility term. Measures of the Kalman filter covariance matrix along with the process itself are used to capture the volatility dynamics for the intravalues of the time-series. The MRSP model also provides for the evolution of the intravalues of the time series. Experimental results are presented demonstrating the applicability of the model using daily data from the Dow Jones Industrial Average (DJIA) time series.