Scholarlink

Abstract <p>A method for constructing empirical autocovariance for a time series with gaps directly in the course of data arrival is considered. The proposed approach uses ideas of information accumulation under conditions of big data. Namely, as data arrive, canonical information of a special form is updated, and the actual autocovariance estimate is computed from it in real time. Therewith, it becomes unnecessary to store old data. As the main application of autocovariance estimate, we consider the problem of optimal estimation of missing fragments. In this work, we investigate the effect of gaps of different types and the fraction of gaps on the accuracy of constructing the autocovariance estimate and consider the effect of these factors on the quality of filling the missing fragments of the time series. It is shown that the autocovariance estimates constructed on the basis of series with a large fraction of often gaps can lose some important properties of autocovariance such as smoothness and positive definiteness, which negatively affects the quality of filling the gaps.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Real-Time Estimation of Autocovariance for Large Time Series with Gaps and Its Application

  • 期刊论文

  • 发表日期：

    2025年9月1日

查看全文
  • P. V. Golubtsov,
  • S. E. Semyonova,
  • N. E. Shapkina,
  • A. I. Chulichkov

摘要

Abstract

A method for constructing empirical autocovariance for a time series with gaps directly in the course of data arrival is considered. The proposed approach uses ideas of information accumulation under conditions of big data. Namely, as data arrive, canonical information of a special form is updated, and the actual autocovariance estimate is computed from it in real time. Therewith, it becomes unnecessary to store old data. As the main application of autocovariance estimate, we consider the problem of optimal estimation of missing fragments. In this work, we investigate the effect of gaps of different types and the fraction of gaps on the accuracy of constructing the autocovariance estimate and consider the effect of these factors on the quality of filling the missing fragments of the time series. It is shown that the autocovariance estimates constructed on the basis of series with a large fraction of often gaps can lose some important properties of autocovariance such as smoothness and positive definiteness, which negatively affects the quality of filling the gaps.