Time-Series Forecasting by Statistical State-Dependent Reconstruction of Coefficients of Itô-Type Processes

We consider the problem of time-series forecasting via statistical reconstruction of the coefficients of the Itô representation of the underlying stochastic process X(t). The reconstructed coefficients are obtained using techniques that account for their dependence on the current value of the process. We augmented the basic linear autoregressive model with the estimated Itô drift coefficients: 1st order a^(t,Xt) and 2nd order a^^(t,a^(t,Xt)) that can be treated as the 1st and 2nd quasi-derivatives of the original time series that is assumed to be a realization of X(t). The predictive techniques used in this paper are based on a kind of statistical analog of the Taylor expansion for the time series. The proposed predictive algorithms demonstrate higher accuracy as compared to other autoregressive algorithms applied to forecasting a big set of time series.