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Inferring time non-homogeneous Ornstein Uhlenbeck type stochastic process. (English) Zbl 1510.60074

Summary: A generalization of the classical Ornstein Uhlenbeck diffusion process including some deterministic time dependent functions in the infinitesimal moments is considered. The inference based on discrete sampling in time is provided by means of an iterative procedure that, in each step, combines the classical maximum likelihood estimation and a generalized method of moments. The validity of the suggested procedure is evaluated via a simulation study by considering several infinitesimal moments for the Ornstein Uhlenbeck type process and taking different sample size. Finally, an application to PM\(_{10}\) daily concentration in Turin metropolitan area in Italy is discussed.

MSC:

60J60 Diffusion processes
62M05 Markov processes: estimation; hidden Markov models
62-08 Computational methods for problems pertaining to statistics
62P12 Applications of statistics to environmental and related topics

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