Inference and first-passage-times for the lognormal diffusion process with exogenous factors: application to modelling in economics (Q2711702)

The homogeneous lognormal diffusion process has been widely used in stochastic modelling in different scientific fields. A non-homogeneous extension of this process is the lognormal process with exogenous factors, applied to the description, forecasting and analysis of growth policy in economic matters. The motivation that leads the authors to include the exogenous factors is to introduce an explanation about the behaviour of the studied variable by the diffusion (endogenous variable) in terms of a set of variables (exogenous variables). These exogenous variables let control the above endogenous variable and their time behaviour is assumed as known. In some practical situations, it has been proved that the trend of some economic variables shows deviations, in certain time intervals, in relation to the exponential shape of the trend of lognormal process. For this reason, one of the most important problems in practice is the suitable choice of the exogenous factors to include in the trend. These factors must contribute to the description of the process evolution as its external control with forecasting aims. The objective of this paper is to show a methodology to build a process of this kind which describes variables with a behaviour as the above mentioned, and to phrase and to find out first-passage-time problem. This methodology is shown by means of an application to real data based on GNP of Spain.