Approximating sums of products of dependent random variables

Lesław Gajek and Elżbieta Krajewska

Statistics & Probability Letters, 2020, vol. 164, issue C

Abstract: Stochastic approximation of a given time series {∑j=1kXjYj} by a linear combination of simpler sequences {∑j=1kXj} and {∑j=1kYj} is treated uniformly over k∈{1,…,n}. A maximal inequality is proven in order to find a sharp bound on Value-at-Risk of max1≤k≤n|∑j=1kXjYj|.

Keywords: Convergence of submartingales; Time series approximation; Sums of products of random variables; Maximal inequalities; Value-at-risk (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108803

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