Maximum likelihood estimation in multivariate lognormal diffusion process with a vector of exogenous factors
- Gutiérrez Jáimez, Ramón
- Gutiérrez Sánchez, Ramón
- Nafidi, Ahmed
- Palacios Latasa, Manuel Pedro (coord.)
- Trujillo, David (coord.)
- Torrens Iñigo, Juan José (coord.)
- Madaune-Tort, Monique (coord.)
- López de Silanes Busto, María Cruz (coord.)
- Sanz Sáiz, Gerardo (coord.)
Editorial: Prensas de la Universidad de Zaragoza ; Universidad de Zaragoza
ISBN: 84-7733-720-9
Año de publicación: 2003
Páginas: 337-346
Congreso: Jornadas Zaragoza-Pau de Matemática Aplicada y Estadística (8. 2003. Jaca)
Tipo: Aportación congreso
Resumen
In this paper we consider a new model of multivariate lognormal diffusion process 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]), extends the possibility of applications of lognormal dynamic modelling in Economics, Population Growth, Volatility,etc.