Fractional Integrals of Stationary Processes and the Central Limit Theorem

Richard A. Davis,Dimitris N. Politis,Keh-Shin Lii

doi:10.1007/978-1-4419-8339-8_29

Fractional Integrals of Stationary Processes and the Central Limit Theorem

Richard A. Davis, Dimitris N. Politis + Show 1 more

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https://doi.org/10.1007/978-1-4419-8339-8_29

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Publication Date: Jan 1, 2011

Affiliation: Columbia University, University of California, San Diego, University of California, Riverside

#Long-range Dependence #Central Limit Theorem + Show 8 more

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Abstract

A class of limit theorems involving asymptotic normality is derived for stationary processes whose spectral density has a singular behavior near frequency zero. Generally these processes have ’long-range dependence’ but are generated from strongly mixing processes by a fractional integral or derivative transformation. Some related remarks are made about random solutions of the Burgers equation.KeywordsFractional IntegralStationary ProcessCentral Limit TheoremSingular SpectrumBurgers Equation

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