Limit theorems for the sample autocovariance of a continuous-time moving average process with long memory

2015/02/17 by Felix Spangenberg, Spangenberg, Felix · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #Advanced Statistical Process Monitoring #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1502.04851

openalex publication_date 2015/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine the asymptotic behaviour of the sample autocovariance in a continuous-time moving average model with long-range dependence. We show that it is either asymptotically Rosenblatt distributed or stable distributed. This shows that results by Horváth and Kokoszka for discrete-time moving average processes with long memory also hold for continuous-time moving average processes.

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