Optimal rates for parameter estimation of stationary Gaussian processes

Khalifa Es-Sebaiy and Frederi G. Viens

Stochastic Processes and their Applications, 2019, vol. 129, issue 9, 3018-3054

Abstract: We study rates of convergence in central limit theorems for partial sums of polynomial functionals of general stationary and asymptotically stationary Gaussian sequences, using tools from analysis on Wiener space. In the quadratic case, thanks to newly developed optimal tools, we derive sharp results, i.e. upper and lower bounds of the same order, where the convergence rates are given explicitly in the Wasserstein distance via an analysis of the functionals’ absolute third moments. These results are tailored to the question of parameter estimation, which introduces a need to control variance convergence rates. We apply our result to study drift parameter estimation problems for some stochastic differential equations driven by fractional Brownian motion with fixed-time-step observations.

Keywords: Central limit theorem; Berry–Esséen; Stationary Gaussian processes; Nourdin–Peccati analysis; Parameter estimation; Fractional Brownian motion (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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DOI: 10.1016/j.spa.2018.08.010

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