Komlós–Major–Tusnády approximation under dependence

By István Berkes, Weidong Liu, Wei Biao Wu. 2014

101 citations recorded by the source corpus.

The celebrated results of Koml\'os, Major and Tusn\'ady [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131; Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] give optimal Wiener approximation for the partial sums of i.i.d. random variables and provide a powerful tool in probability and statistics. In this paper we extend KMT approximation for a large class of dependent stationary processes, solving a long standing open problem in probability theory. Under the framework of stationary causal processes and functional dependence measures of Wu [Proc. Natl. Acad. Sci. USA 102 (2005) 14150-14154], we show that, under natural moment conditions, the partial sum processes can be approximated by Wiener process with an optimal rate. Our dependence conditions are mild and easily verifiable. The results are applied to ergodic sums, as well as to nonlinear time series and Volterra processes, an important class of nonlinear processes.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/213cbe8d93d9127bac56348ed543f11006aa2259

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Citations in the corpus

Extensions of some classical methods in change point analysis (2014, background): “These results can be found in Aue et al. (2006b), Berkes et al. (2014), Bradley (2007), Dedecker et al. (2007), Doukhan (1994) and Eberlein (1986).”