IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v25y2023i2d10.1007_s11009-023-10031-4.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-023-10031-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-023-10031-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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).
    3. 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..
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. Albano, G. & Giorno, V., 2020. "Inferring time non-homogeneous Ornstein Uhlenbeck type stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    9. Bo Martin Bibby & Michael SÛrensen, 1996. "A hyperbolic diffusion model for stock prices (*)," Finance and Stochastics, Springer, vol. 1(1), pages 25-41.
    10. 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.
    11. Nikita Ratanov, 2021. "Ornstein-Uhlenbeck Processes of Bounded Variation," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 925-946, September.
    12. 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.
    13. 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.
    14. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    2. J. Jimenez & R. Biscay & T. Ozaki, 2005. "Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(2), pages 109-141, June.
    3. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2009. "The trend of the total stock of the private car-petrol in Spain: Stochastic modelling using a new gamma diffusion process," Applied Energy, Elsevier, vol. 86(1), pages 18-24, January.
    4. repec:wyi:journl:002108 is not listed on IDEAS
    5. Cai, Lili & Swanson, Norman R., 2011. "In- and out-of-sample specification analysis of spot rate models: Further evidence for the period 1982-2008," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 743-764, September.
    6. Christopher S. Jones, 2003. "Nonlinear Mean Reversion in the Short-Term Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 793-843, July.
    7. Dennis Kristensen, 2007. "Nonparametric Estimation and Misspecification Testing of Diffusion Models," CREATES Research Papers 2007-01, Department of Economics and Business Economics, Aarhus University.
    8. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, October.
    9. Hurn, A.S. & Lindsay, K.A. & McClelland, A.J., 2013. "A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions," Journal of Econometrics, Elsevier, vol. 172(1), pages 106-126.
    10. Cai, Zongwu & Hong, Yongmiao, 2003. "Nonparametric Methods in Continuous-Time Finance: A Selective Review," SFB 373 Discussion Papers 2003,15, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    11. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    12. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July.
    13. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
    14. Wang, Xiaohu & Phillips, Peter C.B. & Yu, Jun, 2011. "Bias in estimating multivariate and univariate diffusions," Journal of Econometrics, Elsevier, vol. 161(2), pages 228-245, April.
    15. Aït-Sahalia, Yacine & Kimmel, Robert L., 2010. "Estimating affine multifactor term structure models using closed-form likelihood expansions," Journal of Financial Economics, Elsevier, vol. 98(1), pages 113-144, October.
    16. Jan Baldeaux & Fung & Katja Ignatieva & Eckhard Platen, 2015. "A Hybrid Model for Pricing and Hedging of Long-dated Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(4), pages 366-398, September.
    17. Zhe Zhao & Zhenyu Cui & Ionuţ Florescu, 2018. "VIX derivatives valuation and estimation based on closed-form series expansions," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 1-18, June.
    18. Peter Spencer, 2004. "Affine Macroeconomic Models of the Term Structure of Interest Rates: The US Treasury Market 1961-99," Discussion Papers 04/16, Department of Economics, University of York, revised Jan 2006.
    19. Kimmel, Robert L., 2007. "Complex Times: Asset Pricing and Conditional Moments under Non-affine Diffusions," Working Paper Series 2007-6, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    20. Ai[dieresis]t-Sahalia, Yacine & Yu, Jialin, 2006. "Saddlepoint approximations for continuous-time Markov processes," Journal of Econometrics, Elsevier, vol. 134(2), pages 507-551, October.
    21. Chew Lian Chua & Sandy Suardi, 2005. "Is There a Unit Root in East-Asian Short-Term Interest Rates?," Melbourne Institute Working Paper Series wp2005n14, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10031-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.