MAXIMUM LIKELIHOOD ESTIMATION IN MULTIVARIATE LOGNORMAL DIFFUSION PROCESSES WITH A VECTOR OF EXOGENOUS FACTORS

Abstract

Abstract. In this paper we consider a new model of multivariate lognormal diffusion pro-cess with a vector of exogenous factors such that each component exclusively affects the respective endogenous variable of the process. Starting from the Kolmogorov differential equations and Ito’s stochastics equation of this model, its transition probability density is obtained. A discrete sampling of the process is assumed and the associated conditioned likelihood is calculated. By using matrix differential calculus, the maximum likelihood matrix estimators are obtained and expressed in a computationally feasible form. This model, an extension of previously studied lognormal diffusion processes ([1],[2],[3]), ex-tends the possibility of applications of lognormal dynamic modelling in Economics, Pop