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A Stochastic Schumacher Diffusion Process: Probability Characteristics Computation and Statistical Analysis

Author

Listed:
  • Ahmed Nafidi

    (Hassan First University of Settat, National School of Applied Sciences)

  • Abdenbi El Azri

    (Hassan First University of Settat, National School of Applied Sciences)

  • Ramón Gutiérrez-Sánchez

    (University of Granada)

Abstract

The principal goal of this article is to establish a methodological approach to computational statistical analysis for a new in-homogeneous stochastic diffusion process with mean function corresponds to the Schumacher curve. Firstly, we analyse the principal probabilistic characteristics like the functions of the mean and the transition probability density of the process. So, the parameters estimation appearing in the current process are determined by the maximum likelihood approach with discrete sampling. Finally, so as to provide the performance of the proposed process, we will apply these computational statistical results to simulated data based on a discretization of the analytical expression of the process by justifying the fit and prediction possibilities.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10031-4
    DOI: 10.1007/s11009-023-10031-4
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    3. Albano, G. & Giorno, V., 2020. "Inferring time non-homogeneous Ornstein Uhlenbeck type stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    4. Bo Martin Bibby & Michael SÛrensen, 1996. "A hyperbolic diffusion model for stock prices (*)," Finance and Stochastics, Springer, vol. 1(1), pages 25-41.
    5. Nafidi, Ahmed & El Azri, Abdenbi, 2021. "A stochastic diffusion process based on the Lundqvist–Korf growth: Computational aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 25-38.
    6. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez & Eva Ramos-Ábalos, 2020. "Stochastic Square of the Brennan-Schwartz Diffusion Process: Statistical Computation and Application," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 455-476, June.
    7. 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.
    8. Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(5), pages 615-645, October.
    9. Merkle, Milan & F. Saporito, Yuri & S. Targino, Rodrigo, 2020. "Bayesian approach for parameter estimation of continuous-time stochastic volatility models using Fourier transform methods," Statistics & Probability Letters, Elsevier, vol. 156(C).
    10. A. Katsamaki & C. H. Skiadas, 1995. "Analytic solution and estimation of parameters on a stochastic exponential model for a technological diffusion process," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(1), pages 59-75, March.
    11. Egorov, Alexei V. & Li, Haitao & Xu, Yuewu, 2003. "Maximum likelihood estimation of time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 114(1), pages 107-139, May.
    12. Rásonyi, Miklós & Tikosi, Kinga, 2022. "On the stability of the stochastic gradient Langevin algorithm with dependent data stream," Statistics & Probability Letters, Elsevier, vol. 182(C).
    13. Nikita Ratanov, 2021. "Ornstein-Uhlenbeck Processes of Bounded Variation," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 925-946, September.
    14. Gutiérrez, R. & Nafidi, A. & Gutiérrez Sánchez, R., 2005. "Forecasting total natural-gas consumption in Spain by using the stochastic Gompertz innovation diffusion model," Applied Energy, Elsevier, vol. 80(2), pages 115-124, February.
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