Extraction of informative statistical features in the problem of forecasting time series generated by It{ô}-type processes
Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics（罗蒙诺索夫莫斯科国立大学，计算数学与 cybernetics 学院）；Moscow Center for Fundamental and Applied Mathematics（莫斯科基础与应用数学中心）；Federal Research Center ‘‘Computer Science and Control’’, Russian Academy of Sciences（俄罗斯科学院计算机科学与控制联邦研究中心）；Moscow Center for Artificial Intelligence（莫斯科人工智能中心）；Vologda State University（沃洛佳州大学）
Victor Korolev, Mikhail Ivanov, Tatiana Kukanova, Artyom Rukavitsa, Alexander Vakshin, Peter Solomonov, Alexander Zeifman
In this paper, we consider the problem of extraction of most informative features from time series that are regarded as observed values of stochastic processes satisfying the It{ô} stochastic differential equations with unknown random drift and diffusion coefficients. We do not attract any additional information and use only the information contained in the time series as it is. Therefore, as additional features, we use the parameters of statistically adjusted mixture-type models of the observed regularities of the behavior of the time series. Several algorithms of construction of these parameters are discussed. These algorithms are based on statistical reconstruction of the coefficients which, in turn, is based on statistical separation of normal mixtures. We obtain two types of parameters by the techniques of the uniform and non-uniform statistical reconstruction of the coefficients of the underlying It{ô} process. The reconstructed coefficients obtained by uniform techniques do not depend on the current value of the process, while the non-uniform techniques reconstruct the coefficients with the account of their dependence on the value of the process. Actually, the non-uniform techniques used in this paper represent a stochastic analog of the Taylor expansion for the time series. The efficiency of the obtained additional features is compared by using them in the autoregressive algorithms of prediction of time series. In order to obtain pure conclusion that is not affected by unwanted factors, say, related to a special choice of the architecture of the neural network prediction methods, we used only simple autoregressive algorithms. We show that the use of additional statistical features improves the prediction.
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Shandong University（山东大学）；Hong Kong University of Science and Technology（香港科技大学）；Didi Chuxing（滴滴出行）；Southern University of Science and Technology（南方科技大学）
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NOVA School of Science and Technology (NOVA FCT)（新里斯本大学科学与技术学院（NOVA FCT））；IPMA - Instituto Português do Mar e da Atmosfera（葡萄牙海洋与大气研究所（IPMA））；NOVA Laboratory for Computer Science and Informatics (NOVA LINCS)（新里斯本大学计算机科学与信息学实验室（NOVA LINCS））；Center for Mathematics and Applications (NOVA Math)（新里斯本大学数学与应用中心（NOVA Math））；NOVA Research & Development Unit for Mechanical and Industrial Engineering (UNIDEMI)（新里斯本大学机械与工业工程研发单元（UNIDEMI））
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Xiaohongshu Inc.（小红书公司）；National University of Singapore（新加坡国立大学）；The City University of New York, CUNY（纽约市立大学，CUNY）；State Key Lab of General AI, School of Intelligence Science and Technology, Peking University（人工智能国家重点实验室，北京大学）；Center for Data Science, Peking University（北京大学数据科学中心）；College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）
