A central limit theorem for the sample autocorrelations of a Lévy driven continuous time moving average process

2012/06/14 by Serge Cohen, Alexander Lindner, Cohen, Serge +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1206.3094

openalex publication_date 2012/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we consider Lévy driven continuous time moving average processes observed on a lattice, which are stationary time series. We show asymptotic normality of the sample mean, the sample autocovariances and the sample autocorrelations. A comparison with the classical setting of discrete moving average time series shows that in the last case a correction term should be added to the classical Bartlett formula that yields the asymptotic variance. An application to the asymptotic normality of the estimator of the Hurst exponent of fractional Lévy processes is also deduced from these results.

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