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Journal of Probability and Statistics
Volume 2016, Article ID 5191583, 8 pages
http://dx.doi.org/10.1155/2016/5191583
Research Article

Parameter Estimation in Mean Reversion Processes with Deterministic Long-Term Trend

Department of Mathematical Sciences, Universidad Eafit, Carrera 49 No. 7 Sur 50, Medellin, Colombia

Received 12 April 2016; Accepted 23 July 2016

Academic Editor: Chin-Shang Li

Copyright © 2016 Freddy H. Marín Sánchez and Verónica M. Gallego. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper describes a procedure based on maximum likelihood technique in two phases for estimating the parameters in mean reversion processes when the long-term trend is defined by a continued deterministic function. Closed formulas for the estimators that depend on observations of discrete paths and an estimation of the expected value of the process are obtained in the first phase. In the second phase, a reestimation scheme is proposed when a priori knowledge exists of the long-term trend. Some experimental results using simulated data sets are graphically illustrated.