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Bayesian inference of fractional brownian motion of multivariate stochastic differential equations | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 201، دوره 13، شماره 1، خرداد 2022، صفحه 2425-2454 اصل مقاله (1.32 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.5944 | ||
| نویسندگان | ||
| Qutaiba N. Nauef Al-Qazaz* ؛ Ahmed H. Ali | ||
| Department of Statistics, University of Baghdad, Iraq | ||
| تاریخ دریافت: 21 اردیبهشت 1400، تاریخ پذیرش: 10 مهر 1400 | ||
| چکیده | ||
| There have been much interest in analysis of stochastic differential equation with long memory, represented by fractional diffusion process, this property have been proved itself in financial mathematic as intrinsic character of financial time series, so finding an appropriate method for estimate and analyze stochastic differential equations with long memory is a very important contemporary topic, in this paper we suggest a method for a system of stochastic differential equations with long memory, also we use the Bayesian methodology to incorporate the advanced knowledge , in addition we apply renormalized integral known in literature as Wick-It\^{o}-Skorohod to solve problem of arbitrage in stochastic models (which yield inefficient mathematical stochastic models for financial market), some of conventional methods like quasi maximum likelihood , Separable Integral-Matching for Ordinary Differential Equations, and multivariate Brownian method are used to be compared with the suggested method. The suggested method has been proved to be very accurate. The estimated model used to calculate the portfolio of assets quantities allocation. | ||
| کلیدواژه‌ها | ||
| Fractional Brownian motion؛ stochastic differential equations؛ maximum likelihood؛ prior distribution؛ Metropolis Hasting method؛ Hurst index؛ Langevin method | ||
| مراجع | ||
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[1] Q. N. Al-Kazaz and H. J. K. Al-Saadi, Comparing Bayes estimation with Maximum Likelihood Estimation of Generalized Inverted Exponential Distribution in Case of Fuzzy Data, J. Econ. Administrative Sci. , 23 (101) (2017). [2] A. H. Ali and Q. N. N. AL-Qazaz, Fractional Brownian motion inference of multivariate stochastic differential equations, Periodicals of Eng. Nat. Sci.,8 (2020) 464-480. [3] P. O. Amblard, J. F. Coeurjolly, Identification of the Multivariate Fractional Brownian Motion, IEEE Trans. Signal Process., 59(2011) 5152-5168. [4] P. O. Amblard, C. J. Fran¸cois, F. Lavancier and A. Philippe, Basic properties of the Multivariate Fractional Brownian Motion, S´eminaires et congr`es, Soci´et´e math´ematique de France, 28(2013) 65-87 . [5] F. Biagini, Y. Hu, B. Øksendal and T. Zhang, Stochastic Calculus for Fractional Brownian Motion and Applications, Springer, 2008. [6] J. Beran, Statistics for Long-Memory Processes, Chapman & Hall Imp An Int. Thomson Publishing Company, 1994. [7] Y. Chang, Efficiently Implementing the Maximum Likelihood Estimator for Hurst Exponent, Hindawi Publishing Corporation, Math. Prob. Eng., 2014 (2014), Article ID 490568. [8] J. Coeurjolly, P. Amblard and S. Achard, On multivariate fractional Brownian motion and multivariate fractional Gaussian noise, In: 2010 18th European Signal Process. Conf., Aalborg, 2010, pp. 1567-1571 . [9] H. Haario, E. Saksman and J. Tamminen, Adaptive proposal distribution for random walk Metropolis algorithm, Bernoulli, 2001. [10] Y. Hu and B. Øksendal, Fractional white noise calculus and applications to finance, Infinite Dimensional Analysis, Quantum Probability and Related Topics, World Scientific Publishing Company, 6 (1)(2003) 1-32, . [11] S. Iacus and N. Yoshida, Simulation and Inference for Stochastic Processes with YUIMA, Springer 2018. [12] A. Iranmanesh, M. Arashi, S. M. M. Tabatabaey, On Conditional Applications of Matrix Variate Normal Distribution. Iran. J. Math. Sciences and Inf., 5 (2)(2010) 33-43. [13] M. Krzywda, Fractional Brownian Motion and applications to financial modeling, Jagiellonian University, Mathematics and Computer Science, Institute of Mathematics, Master Thesis, 2011. [14] F. Lavancier, A. Philippe and D. Surgailis, Covariance function of vector self-similar process, Stat. Probab. Lett., 79 (2009). [15] T. lundahl and W. ohley, Fractional Brownian Motion: A Maximum Likelihood Estimator and Its Application to Image Texture, IEEE Trans. Med. Imaging, mi-5 (3)(1986) 152-161 . [16] H. Markowitz, Portfolio Selection, J. Finance, 7 (1)(1952) 77-91. [17] S. K. Mitra, A density-free approach to matrix variate beta distribution, Indian J. Stat., Ser. A, 32 (1)(1970) 81-88. [18] A. Pedersen, A New Approach to Maximum Likelihood Estimation for Stochastic Differential Equations Based on Discrete Observations, Scand. J. Stat., 22 (1)(1995) 55-57 . [19] B. Pfaff, Financial Risk Modeling and Portfolio Optimization with R, 2nd Edition, Wiley & Sons, 2013. [20] P. Rinng, P. Lind, M. Wachter and J. Peinke, The Langevin Approach: An R Package for Modeling Markov Processes, Cornell Univ., Physics. data-an, 2016. [21] R. Yaari and I. Dattner, Simode: R Package for statistical inference of ordinary differential equations using separable integral-matching, 2019. [22] G. Lim, S. Yong, J. Zhou, S. Yoon, J. Won and K. Kim, Dynamical Stochastic Processes of Returns in Financial Markets, Elsevier, Physica A: Stat. Mech. its Appl., 376 (1)(2005) 517-524. | ||
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