Apostolos P. Leros, Athina P. Bougioukou, And Theodoros I. Maris

In this paper a mean reverting stochastic process (MRSP) model is presented for generating intravalues of time series. 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. The applicability of the model is demonstrated using the daily Dow Jones Industrial Average (DJIA) time series


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