Elements of Randomized Forecasting and Its Application to Daily Electrical Load Prediction in a Regional Power System
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TELLECTUAL CONTROL SYSTEMS, DATA ANALYSIS
Elements of Randomized Forecasting and Its Application to Daily Electrical Load Prediction in a Regional Power System Yu. S. Popkov∗,∗∗,a , A. Yu. Popkov∗,b , and Yu. A. Dubnov∗,∗∗∗,c ∗
Federal Research Center “Information Science and Control,” Russian Academy of Sciences, Moscow, Russia ∗∗ Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia ∗∗∗ National Research University Higher School of Economics, Moscow, Russia e-mail: a [email protected], b [email protected], c [email protected] Received October 14, 2019 Revised December 11, 2019 Accepted January 30, 2020
Abstract—A randomized forecasting method based on the generation of ensembles of entropyoptimal forecasting trajectories is developed. The latter are generated by randomized dynamic regression models containing random parameters, measurement noises, and a random input. The probability density functions of random parameters and measurement noises are estimated using real data within the randomized machine learning procedure. The ensembles of forecasting trajectories are generated by the sampling of the entropy-optimal probability distributions. This procedure is used for the randomized prediction of the daily electrical load of a regional power system. A stochastic oscillatory dynamic regression model is designed. One-, two-, and three-day forecasts of the electrical load are constructed, and their errors are analyzed. Keywords: forecasting, hierarchical randomization, oscillatory dynamic regression, entropy functional, empirical balance, daily electrical load of power system, sampling of probability density functions DOI: 10.1134/S0005117920070103
1. INTRODUCTION The traditional way to solve forecasting problems consists of the following. First of all, an appropriate model is constructed for the process under study. Then this parameterized model is learned on retrospective information. Finally, the learned model as used as a forecasting one. Hence, the forecasting of dynamic processes includes two main stages, machine learning of the process model and forecasting itself. The modern concept of machine learning is based on the deterministic parametrization of models and parameter estimates using data sets with postulated properties. The quality of estimation is characterized by empirical risk functions, and their minimization gives optimal estimates [1, 2]. Parametric dynamic regression models (PDRMs) are most widespread representatives of this class, in which the current state of a model is determined by its past states on a certain time interval [3, 4]. A formal image of PDRMs is difference equations, in the general case of the pth order [5]. Most applications are described by linear PDRMs. In particular, they naturally occur in many problems of macroeconomic modeling and forecasting, e.g., time series analysis of economic indices [6], adequacy analysis of PDRMs [7], and prediction of exchange rates [8]. Linear PDRMs are effective enough for short-term forecasting, albeit causing si
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