Gompertz Stochastic Differential Equation Growth Model with Exogenous Variables and Time-Dependent Diffusion

Abstract

Gutierrez et al. (2005) studied Gompertz homogeneous diffusion process with exogenous variables that affect the trend. The purpose of present article is to modify this work in two directions. The first one is that the diffusion term is taken as time-dependent, which is more realistic. Another direction of modification is that the powerful technique of Wavelet analysis is employed to estimate the drift term, rather than the elementary piecewise time-varying linear functions approach. The methodology, after incorporating the above two aspects is developed. Relevant computer programs for its application are written and the same are included as an Appendix. Finally, as an illustration, India’s total foodgrain production time-series data dependent on rainfall, fertilizer, and pesticide time-series data as exogenous variables are considered and superiority of our proposed model is shown over the model proposed by Gutierrez et al. (2005) for given data.