Parameter estimation for the Langevin equation with stationary-increment Gaussian noise

Tommi Sottinen () and Lauri Viitasaari ()
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Tommi Sottinen: University of Vaasa
Lauri Viitasaari: Aalto University School of Science, Helsinki

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 3, No 6, 569-601

Abstract: Abstract We study the Langevin equation with stationary-increment Gaussian noise. We show the strong consistency and the asymptotic normality with Berry–Esseen bound of the so-called second moment estimator of the mean reversion parameter. The conditions and results are stated in terms of the variance function of the noise. We consider both the case of continuous and discrete observations. As examples we consider fractional and bifractional Ornstein–Uhlenbeck processes. Finally, we discuss the maximum likelihood and the least squares estimators.

Keywords: Gaussian processes; Langevin equation; Ornstein–Uhlenbeck processes; Parameter estimation; 60G15; 62M09; 62F12 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11203-017-9156-6

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