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Inference with Non-Homogeneous Lognormal Diffusion Processes Conditioned on Nearest Neighbor

Author

Listed:
  • Ana García-Burgos

    (Departamento de Estadística e IO, Universidad de Granada, 18012 Granada, Spain)

  • Paola Paraggio

    (Dipartimento di Matematica, Università di Salerno, 84084 Fisciano, Italy)

  • Desirée Romero-Molina

    (Departamento de Estadística e IO, Universidad de Granada, 18012 Granada, Spain)

  • Nuria Rico-Castro

    (Departamento de Estadística e IO, Universidad de Granada, 18012 Granada, Spain)

Abstract

In this work, we approach the forecast problem for a general non-homogeneous diffusion process over time with a different perspective from the classical one. We study the main characteristic functions as mean, mode, and α -quantiles conditioned on a future time, not conditioned on the past (as is normally the case), and we observe the specific formula in some interesting particular cases, such as Gompertz, logistic, or Bertalanffy diffusion processes, among others. This study aims to enhance classical inference methods when we need to impute data based on available information, past or future. We develop a simulation and obtain a dataset that is closer to reality, where there is no regularity in the number or timing of observations, to extend the traditional inference method. For such data, we propose using characteristic functions conditioned on the past or the future, depending on the closest point at which we aim to perform the imputation. The proposed inference procedure greatly reduces imputation errors in the simulated dataset.

Suggested Citation

  • Ana García-Burgos & Paola Paraggio & Desirée Romero-Molina & Nuria Rico-Castro, 2024. "Inference with Non-Homogeneous Lognormal Diffusion Processes Conditioned on Nearest Neighbor," Mathematics, MDPI, vol. 12(23), pages 1-23, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3703-:d:1529986
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    References listed on IDEAS

    as
    1. Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2018. "Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors," Mathematics, MDPI, vol. 6(5), pages 1-13, May.
    2. Román-Román, P. & Torres-Ruiz, F., 2015. "A stochastic model related to the Richards-type growth curve. Estimation by means of simulated annealing and variable neighborhood search," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 579-598.
    3. Antonio Di Crescenzo & Paola Paraggio & Serena Spina, 2023. "Stochastic Growth Models for the Spreading of Fake News," Mathematics, MDPI, vol. 11(16), pages 1-23, August.
    4. Antonio Di Crescenzo & Paola Paraggio & Patricia Román-Román & Francisco Torres-Ruiz, 2023. "Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean," Statistical Papers, Springer, vol. 64(5), pages 1391-1438, October.
    5. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    6. Román, P. & Serrano, J.J. & Torres, F., 2008. "First-passage-time location function: Application to determine first-passage-time densities in diffusion processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 4132-4146, April.
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