%0 Journal Article
%T Gaussian Estimation of One-Factor Mean Reversion Processes
%A Freddy H. Mar¨ªn S¨¢nchez
%A J. Sebastian Palacio
%J Journal of Probability and Statistics
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/239384
%X We propose a new alternative method to estimate the parameters in one-factor mean reversion processes based on the maximum likelihood technique. This approach makes use of Euler-Maruyama scheme to approximate the continuous-time model and build a new process discretized. The closed formulas for the estimators are obtained. Using simulated data series, we compare the results obtained with the results published by other authors. 1. Introduction Different applications of stochastic differential equations have attracted the attention of many researchers in relation to the theoretical advances needed for modeling and simulation of the dynamic behavior of the main variables affecting the evolution of some phenomena. Applications in fields of economics, finance, physics, insurance, and others have been drivers of these developments. Particularly, through diffusion processes have been carried out modeling interest rates and commodity prices, where they used in their modeling processes mean reversion. Some trends of these studies are based on some a priori knowledge to determine the structure of the model to be used, while other alternatives are part of a general structure, and statistical procedures through the particular structure are determined to represent the phenomenon. Whichever approach is used, in general, in the specification of the model, it is necessary to estimate parameters to achieve a proper fit of the model. Although some parameter estimation methods have been extensively studied in diffusion processes, this has a serious problem, which is that the specification of the models is done in continuous time but the data that is available for adjusting the parameters are discretely sampled in time. A common solution to this problem is to discretize the continuous-time model based on Euler-Maruyama scheme and perform procedures on the theoretical formulation resulting in discrete time. From this scheme alternatives can be proposed for parameter estimation approach among which stands out the maximum likelihood estimation. Following the classification proposed by Yu and Phillips [1], different parameter estimation procedures can be classified globally into three categories according to how to proceed from the model formulation: discretization of continuous process and estimation of the parameters with the resulting discretized process, estimation of the transition probability function for the continuous-time model, and independent estimations of the trend and volatility components by kernel methods. Thus, among the methods that are based on the
%U http://www.hindawi.com/journals/jps/2013/239384/