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On the Efficiency and Robustness of Commingle Wiener and Lévy Driven Processes for Vasciek Model
Authors: Rasaki O. Olanrewaju
Abstract:The driven processes of Wiener and Lévy are known self-standing Gaussian-Markov processes for fitting non-linear dynamical Vasciek model. In this paper, a coincidental Gaussian density stationarity condition and autocorrelation function of the two driven processes were established. This led to the conflation of Wiener and Lévy processes so as to investigate the efficiency of estimates incorporated into the one-dimensional Vasciek model that was estimated via the Maximum Likelihood (ML) technique. The conditional laws of drift, diffusion and stationarity process was ascertained for the individual Wiener and Lévy processes as well as the commingle of the two processes for a fixed effect and Autoregressive like Vasciek model when subjected to financial series; exchange rate of Naira-CFA Franc. In addition, the model performance error of the sub-merged driven process was miniature compared to the self-standing driven process of Wiener and Lévy.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.2021739Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 259
 M.S. Ldeo, An Introduction to Dynamical Systems and Chaos, 1997.
 J. Gleick, C. Penguin, Q172.5.C45G54, 1987.
 S. Roweis, Z. Ghahramani, An EM algorithm for identification of non-linear dynamical systems. Gatsby Computational Neuroscience Unit, University College London, London WCIN 3AR, U.K, 2010. http://gatsby.ucl.ac.uk.s
 D. Grahova, N.N. Leonenko, A. Sikorskii, M.S. Taqqu, “The unusual properties of aggregated superpositions of Ornstein–Uhlenbeck type Processes,” Bernoulli, 2017, pp. 1-34.
 C. Lee, J.P.N. Bishwal, M.H. Lee, “Sequential maximum likelihood estimation for reflected Ornstein - Uhlenbeck processes,” Journal of Statistics Planning Inference, vol.142, 2012, pp. 1234-1242.
 R. Kleeman, “Information theory and dynamical system predictability,” Entropy, vol. 13, 2011, pp. 612-649. doi:10.3390/e13030612.
 E. Bibbona, G. Panfilo, P. Tavella, “The Ornstein–Uhlenbeck process as a model for filtered white noise,” dell’Universit di Torino, vol. 45, 2008, pp. 117-126. doi:10.1088/0026-1394/45/6/S17.
 G.E. Uhlenbeck, L.S. Ornstein, Physical Review, vol. 36, 1930, pp. 823-84.
 S. Kullback, R.A. Leibler, “On information and sufficiency,” Annals of Mathematical Statistics,vol. 22 (1), 1951, pp.7986.
 C. Archambeau, D. Cornford, M. Opper, J. Shawe-Taylor, “Gaussian process approximations of stochastic dierential equations,” JMLR: Workshop and Conference Proceedings 1:,2007,1-16.
 L. Eyinck, O. Gregory, R.R. Juan, “Most probable histories for nonlinear dynamics: tracking climate transitions,” Journal of Statistical Physics, vol.101, 2004, 459472.
 A. Apte, M. Hairer, A. Stuart, J. Voss, “Sampling the posterior: An approach to non–Gaussian data assimilation,” Physica D, 2006, Submitted, available from http://www.maths.warwick.ac.uk/ stuart/sample.html.
 O¨ . O¨ nalan, “Financial Modelling with OrnsteinUhlenbeck processes driven by L´evy process”, Proceedings of the World Congress on Engineering, Vol. II, WCE 2009, London, U.K.
 L. Valdivieso, W. Schoutens, F. Tuerlinckx, “Maximum likelihood estimation in processes of Ornstein-Uhlenbeck type,” Stat. Infer. Stoch. Process, vol.12, 2009, 119. doi: 10.1007/s11203-008-9021-8.
 A. Kyprianou, Introductory lectures on fluctuations of L´evy processes with applications, Springer, 2006.
 O.I. Shittu, O.O. Otekunrin, C.G. Udomboso, K. Adepoju, Introduction to probability and stochastic processes with applications, 2014, ISBN 978-978-2890-0-8.