Precursive trend analysis

In this paper, forecasting using the precursive trend is discussed. Two different models of relation between the forecasted value and another parameter (precursive indicator) are considered. For the first model (dynamic linear), the method of forecast operator construction is presented, using the transfer function and Box–Jenkins approach. For the second model (static non-linear), an estimation method of model parameters, assuming that input is a stochastic process with normal distribution, is proposed. This method is based on a relation between autocorrelation functions of input and output and the corresponding rotation of coordinate axes. Two examples are given: in the first, for simple input–output model, an analytical solution is obtained; in the second, for a segmented linear model and approximation of probability distribution function using Hermitian polynomials, a procedure for estimation of parameters is proposed.