Simulating Rubber Prices under Geometric Fractional Brownian Motion with Different Hurst Estimators


  • Srivennila Sri Balasubramaniam aDepartment of Mathematical Science, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Siti N. Ibrahim ᵇDepartment of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia; ᶜInstitute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia



Rubber Prices, Geometric Brownian Motion, Geometric Fractional Brownian Motion, Hurst Exponent


Natural rubber was a vital pillar of Malaysia's export-oriented economy throughout much of the twentieth century, according to the Economic History of Malaya (EHM) website, the worldwide demand for natural rubber is expected to expand at a CAGR of 4.8% in the future (2019–2023). Therefore, it could be concluded that rubber is one of the commodities that should be monitored. Thus, the forecasting of the rubber price should be analysed for the future use. This research focuses on the simulation of rubber prices using geometric Brownian motion and geometric fractional Brownian motion. Moreover, an analysis in the value of hurst exponents' estimator were also done using 3 different methods, Rescaled Range Analysis, Aggravate Variance Method, and Residuals of Regression Method that bases on the slope deviation technique. Finally, an error analysis was done by the calculation of Mean Absolute Percentage Error (MAPE) value to analyse the accuracy of the simulation models.


Malaysia External Trade Statistics Bulletin, June 2021 28 July 2021. [Online]. Available: [Accessed 26 December 2022].

E. Valkeila. (2010). On the approximation of geometric fractional brownian motion. Optimality and Risk - Modern Trends in Mathematical Finance: The Kabanov Festschrift, Berlin, Heidelberg, Springer Berlin Heidelberg, 251-266.

K. Hamed, A. G. Awadallah, E. Brown, S. Hurst and J. Sutcliffe. (2016). Harold Edwin Hurst: the Nile and Egypt, past and future. Hydrological Sciences Journal, 61(9), 1557-1570.

T. Graves, R. Gramacy, N. W. Watkins and C. F. Franzke. (2017). A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA, 1951-1980, Entropy, 19, 437.

S. Aref. (1998). Hurst phenomenon and fractal dimensions in long-term yield data. Conference on Applied Statistics in Agriculture.

B.-R. Cristina-MariaPăcurar. (2020). An analysis of COVID-19 spread based on fractal interpolation and fractal dimension. Chaos, Solitons & Fractals,139, 110073.

L. G. Malaysia. Malaysian Rubber Board. [Online]. Available:

C. Chen. (2022). MATLAB Central File Exchange. [Online]. Available: [Accessed 2022].

A. Hibtallah and M. Y. Hmood. (2021). Comparison of Hurst exponent estimation methods. Journal of Economics and Administrative Sciences, 27, 167-183.

J. Kuepper. (2022)., Investopedia, July 2022. [Online]. Available:

R. M. Bryce and K. B. Sprague. (2012). Revisiting detrended fluctuation analysis. Scientific reports, 2, 315.

R. F. Ceballos and F. F. Largo. (2017). On the estimation of the hurst exponent using adjusted rescaled range analysis, detrended fluctuation analysis and variance time plot: a case of exponential distribution," Imperial Journal of Interdisciplinary Research (IJIR), 3, 424-434.

Z. N. Hamdan, S. N. I. Ibrahim and M. S. Mustafa. (2020). Modelling Malaysian gold prices using geometric brownian motion model. Advances in Mathematics: Scientific Journal. 9, 7463-7469.

S. N. I. Ibrahim, M. Misiran and M. F. Laham. (2020). Geometric fractional Brownian motion model for commodity market simulation. AEJ - Alexandria Engineering Journal, 60, 11.

W. F. Agustini, I. R. A. Affianti and E. R. Putri. (2018). Stock price prediction using geometric Brownian motion. Journal of Physics: Conference Series, 974, 012047.

M. Y. Hmood and A. Hibtallah. (2021). Comparison of Hurst exponent estimation methods. Journal of Economics and Administrative Sciences, 27, 167-183.

D. W. and C. Heyde. (1996). Itô's formula with respect to fractional Brownian motion and its application. Journal of Applied Mathematics and Stochastic Analysis, 9, 01.