Online Program Home
My Program

Abstract Details

Activity Number: 180
Type: Contributed
Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
Sponsor: Business and Economic Statistics Section
Abstract #321308 View Presentation
Title: Intermittency of Superpositions of Ornstein-Uhlenbeck (OU)--Type Processes
Author(s): Irena Tesnjak* and Danijel Grahovac and Alla Sikorskii and Nikolai Leonenko
Companies: Michigan State University and J.J. Strossmayer University of Osijek and Michigan State University and Cardiff University
Keywords: Ornstein-Uhlenbeck type processes ; Intermittency ; long-range dependence ; weak convergence

The superpositions of OU type processes driven by Levy noise have been used extensively to model phenomena with an empirical need for non-Gaussian marginal distributions (MD). Tractability of MD and dependence structure promotes efficient practical implementation. Central limit theorem (CLT) type results allow to construct confidence intervals and perform hypotheses tests for model parameters. This paper deals with weak convergence properties of partial sums of infinite long-range dependent (LRD) discrete superpositions of OU type processes. While it has been proven that limit distributions of finite discrete superpositions are Gaussian, the weak limits for infinite superpositions have not been established. We show that, while partial sums of finite superpositions obey the CLT, the partial sums of infinite LRD superpositions are intermittent, which likely precludes CLT-type results. Intermittency is characterized by progressive growth of moments which, implies unusual limiting behavior of the partial sums. We also present different techniques for simulating these type of processes to illustrate the intermittent behavior. An application of these models to real data is provided.

Authors who are presenting talks have a * after their name.

Back to the full JSM 2016 program

Copyright © American Statistical Association