Forecasting the change in the parameters of time series and continuous functions

Various classes of algorithms for predicting changes in the parameters of continuous functions and time series that occur in the interval called the prediction horizon are considered. The limited possibilities of methods of decomposition of processes into empirical modes and parametric prediction methods based on the representation of the time series by a generalized polynomial in a system of linearly independent functions are shown. Prognosis algorithms based on autoregression models are obtained. Recurrent equations are obtained that determine the explicit dependence of the estimates of the forecast on the coefficients of the model. The questions of finding estimates of the forecast by minimizing the loss function - the square of the norm of deviation of estimates from the observed values of the time series are considered. The method of generalizing the forecasting algorithm using a linear model represented by functional series or artificial neural network (ANN) is investigated. The system of forecasting with the help of ANN is presented.