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Inferring time non-homogeneous Ornstein Uhlenbeck type stochastic process

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  • Albano, G.
  • Giorno, V.

Abstract

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 PM10 daily concentration in Turin metropolitan area in Italy is discussed.

Suggested Citation

  • Albano, G. & Giorno, V., 2020. "Inferring time non-homogeneous Ornstein Uhlenbeck type stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:csdana:v:150:y:2020:i:c:s0167947320300992
    DOI: 10.1016/j.csda.2020.107008
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    References listed on IDEAS

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    1. Albano, Giuseppina & Giorno, Virginia & Román-Román, Patricia & Torres-Ruiz, Francisco, 2012. "Inference on a stochastic two-compartment model in tumor growth," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1723-1736.
    2. Nafidi, A. & Gutiérrez, R. & Gutiérrez-Sánchez, R. & Ramos-Ábalos, E. & El Hachimi, S., 2016. "Modelling and predicting electricity consumption in Spain using the stochastic Gamma diffusion process with exogenous factors," Energy, Elsevier, vol. 113(C), pages 309-318.
    3. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
    4. Giorno, Virginia & Román-Román, Patricia & Spina, Serena & Torres-Ruiz, Francisco, 2017. "Estimating a non-homogeneous Gompertz process with jumps as model of tumor dynamics," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 18-31.
    5. Giuseppina Albano & Michele La Rocca & Cira Perna, 2019. "Small sample properties of ML estimator in Vasicek and CIR models: a simulation experiment," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 5-19, June.
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    Cited by:

    1. D'Auria, Bernardo & Guada, Abel, 2021. "Some results on optimally exercising American put options for time-inhomogeneous processes," DES - Working Papers. Statistics and Econometrics. WS 33130, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Ahmed Nafidi & Abdenbi El Azri & Ramón Gutiérrez-Sánchez, 2023. "A Stochastic Schumacher Diffusion Process: Probability Characteristics Computation and Statistical Analysis," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-15, June.

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