Moderate deviations for non-linear functionals and empirical spectral density of moving average processes

2004/05/27 by Hacène Djellout, Arnaud Guillin, Djellout, Hacene +3
Economics, Econometrics and Finance · Mathematics · #60F10 #60G10 #60G15 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.math/0405521

openalex publication_date 2004/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random variables and the continuity, or weaker, of the spectral density of the moving average process. We also obtain the moderate deviations for the empirical spectral density, exhibiting an interesting new form of the rate function, i.e. with a correction term compared to the Gaussian rate functionnal.

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