This article is cited in 2 papers

Short Communications

Modeling and fitting of time series with heavy distribution tails and strong time dependence by Gaussian time series

A. E. Mazur

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In the model of Gaussian copula time series with the tails of one-dimensional distributions belonging to the Fréchet maximum domain of attraction and the description of dependency based on Gaussian variables (see [A. E. Mazur and V. I. Piterbarg, Moscow Univ. Math. Bull., 70 (2015), pp. 197–201]), an estimator for the copula (which is a nonlinear function that takes Gaussian variables to variables from the Fréchet maximum domain of attraction) is built. This opens the way for statistical analysis of data time series with potentially heavy tails using the machinery of asymptotic analysis of Gaussian sequences. The consistency and asymptotic normality for this estimator are proved.

Keywords: Gaussian sequence, Fréchet maximum domain of attraction, empirical quantile function.

Received: 10.10.2017
Revised: 19.10.2017
Accepted: 23.10.2017

DOI: 10.4213/tvp5158

 English version: Theory of Probability and its Applications, 2018, 63:1, 151–154

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