Algorithm AS 309: Estimation in Multivariate Log‐normal Diffusion Processes with Exogenous Factors

One-dimensional log-normal di€usion processes have been widely studied and applied to several problems in economics (Tintner and Sengupta, 1972; Tintner and Go mez, 1979). Recently Gutie rrez et al. (1991) have studied the multivariate log-normal di€usion process with exogenous factors by using discrete sampling. This work included a program for inference on the parameters of the exogenous factors. In this paper we propose an ampli®cation of this program, including Neudecker's calculus and tests of hypotheses for the parameters (using also discrete sampling). H be a k-dimensional vector whose components are the variables of the process, which we name the endogenous variables, and let F i …t† …i ˆ 1, X X X, p† denote p real-valued functions in [0, T] that constitute the exogenous factors.