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Proceedings of the 17th Conference on Computer Science and Intelligence Systems

Annals of Computer Science and Information Systems, Volume 30

Parameters Estimation of a Lotka-Volterra Model in an Application for Market Graphics Processing Units

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DOI: http://dx.doi.org/10.15439/2022F61

Citation: Proceedings of the 17th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 30, pages 935938 ()

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Abstract. In this paper, a least squares method is used to estimate parameter values in the Lotka-Volterra model. The data used are graphics processing units (GPU) shipment worldwide by three key competitors, namely Nvidia, Intel, and AMD. The goal is to quantify the parameter values of a model with minimal error to qualitatively solve the problem and fit the raw data as closely as possible. Based on the real measurements, the predator between the competitors is recognized through the identification procedure comparing the sign of the coefficients with the original Lotka-Volterra model structure.

References

  1. P. Mercorelli, “A Hysteresis Hybrid Extended Kalman Filter as an Observer for Sensorless Valve Control in Camless Internal Combustion Engines,” IEEE Trans on Ind. Appl., vol. 48, no. 6, pp. 1940–1949, 2012. [Online]. Available: https://doi.org/10.1109/TIA.2012.2226193
  2. P. Mercorelli, “A Two-Stage Augmented Extended Kalman Filter as an Observer for Sensorless Valve Control in Camless Internal Combustion Engines,” IEEE Trans on Ind. Elects, vol. 59, no. 11, pp. 4236–4247, 2012. [Online]. Available: https://doi.org/10.1109/TIE.2012.2192892
  3. K. Benz, C. Rech, and P. Mercorelli, “Sustainable Management of Marine Fish Stocks by Means of Sliding Mode Control,” pp. 907–910, 2019. [Online]. Available: http://dx.doi.org/10.15439/2019F221
  4. P. Klopper and J. Greeff, “Lotka-Volterra model parameter estimation using experiential data,” Applied Mathematics and Computation, vol. 224, pp. 817–825, 2013. [Online]. Available: https://doi.org/10.1016/j.amc.2013.08.093
  5. K. Benz, C. Rech, P. Mercorelli, and O. Sergiyenko, “Two Cascaded and Extended Kalman Filters Combined with Sliding Mode Control for Sustainable Management of Marine Fish Stocks,” Journal of Automation, Mobile Robotics and Intelligent Systems, pp. 28–35, Jul. 2019. [Online]. Available: https://doi.org/10.14313/jamris/3-2020/30
  6. C. Michalakelis, T. Sphicopoulos, and D. Varoutas, “Modeling Competition in the Telecommunications Market Based on Concepts of Population Biology,” IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), vol. 41, no. 2, pp. 200–210, 2011. [Online]. Available: https://doi.org/10.1109/tsmcc.2010. 2053923
  7. J. P. N. Bishwal, Parameter estimation in stochastic differential equations, 2008th ed., ser. Lecture Notes in Mathematics. Berlin, Germany: Springer, Oct. 2007.
  8. X. Zhang, R. D. Brooks, and M. L. King, “A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation,” Journal of Econometrics, vol. 153, no. 1, pp. 21–32, Nov. 2009. [Online]. Available: https://doi.org/10.1016/j.jeconom.2009.04.004
  9. W. Xiao, W. Zhang, and W. Xu, “Parameter estimation for fractional Ornstein–Uhlenbeck processes at discrete observation,” Applied Mathematical Modelling, vol. 35, no. 9, pp. 4196–4207, Sep. 2011. [Online]. Available: https://doi.org/10.1016/j.apm.2011.02.047
  10. J. Yu and P. C. B. Phillips, “A Gaussian approach for continuous time models of the short-term interest rate,” The Econometrics Journal, vol. 4, no. 2, pp. 210–224, Dec. 2001. [Online]. Available: https://doi.org/10.1111/1368-423x.00063
  11. R. Faff and P. Gray, “On the estimation and comparison of short-rate models using the generalised method of moments,” Journal of Banking & Finance, vol. 30, no. 11, pp. 3131–3146, Nov. 2006. [Online]. Available: https://doi.org/10.1016/j.jbankfin.2005.09.016
  12. G. D. Rossi, “Maximum Likelihood Estimation of the Cox–Ingersoll-Ross Model Using Particle Filters,” Computational Economics, vol. 36, no. 1, pp. 1–16, Mar. 2010. [Online]. Available: https: //doi.org/10.1007/s10614-010-9208-0
  13. Statista, “PC GPU shipment share worldwide Q2 2009 - Q3 2021, by vendor,” 2021, data retrieved from Statista, https://www.statista.com/statistics/754557/worldwide-gpu-shipments-market-share-by-vendor/.
  14. D. Chicco, M. J. Warrens, and G. Jurman, “The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation,” vol. 7, p. e623. [Online]. Available: https://doi.org/10.7717/peerj-cs.623