Predictive Model of Energy Market Indicators Based on Continued Approximation for Series Sample Prior to the Moment of Prediction

摘要

Autoregression models use a linear combination of previous time series as a prediction. This article suggests a prediction algorithm based on creating approximation of prior series sample as a linear combination of an existing set of samples. Here, prediction is an obtained linear combination of the continuations of approximating samples. The problem of finding the coefficients of the linear combinations is written as an A. N. Tikhonov's extremum problem of least-squares with a regularizer, which allows creating a system of equations for evaluating the unknown parameters. Solving the system of equations is carried out using the singular spectrum analysis (SSA). Regularity helps to increase the solving quality in noisy conditions. After isolating the singular components of the system of equations matrix, the solution can be obtained in analytical form. The parameters governing the quality of the solution are the regularization coefficients and the set of components of the singular decomposition. The prediction efficiency index is estimated based on the discrepancies between the prediction and actual values of the series for the given depth of the prediction. The prediction model search is done by choosing the best model on the set of values of the regularization parameter with different sets of eigenvectors that determine the solution space. The proposed method was tested on different time series. The examples of prediction of the energy market indicators prove its effectiveness.