A. Nafidi

INFERENCE IN GOMPERTZ-TYPE NONHOMOGENEOUS STOCHASTIC SYSTEMS BY MEANS OF DISCRETE SAMPLING

ABSTRACT We consider an extension of the Gompertz homogeneous diffusion process by introducing time functions (exogenous factors) that affect its trend. After obtaining its transition probability density function, the inference on the parameters of the process is obtained by considering discrete sampling of the sample paths. Finally, we apply this stochastic process to model housing price in Spain.

Detection, modelling and estimation of non-linear trends by using a non-homogeneous Vasicek stochastic diffusion. Application to CO2 emissions in Morocco

This paper proposes a new stochastic model, based on a Vasicek non-homogeneous diffusion process, in which the non-linear trend coefficient (drift) depends on deterministic functions that describe the dynamic evolution of certain exogenous variables. After studying its probabilistic characteristics, and in particular the transition probability density and trend function, the associated stochastic inference based on discrete sampling in time is established using maximum likelihood methodology. This model is applied to detect, estimate and model the non-linear trend present in data corresponding to CO2 emissions in Morocco. Energy and financial variables that affect the behaviour of this trend are also detected, and substantial improvement provided by this non-homogeneous model with respect to its corresponding homogeneous version, is confirmed.

Three-parameter stochastic lognormal diffusion model: statistical computation and simulating annealing – application to real case

In this paper, we propose a new study of a stochastic lognormal diffusion process (SLDP), with three parameters, which can be considered as an extension of the bi-parametric lognormal process with the addition of a threshold parameter. From the Kolmogorov equation, we obtain the probability density function and the moments of this process. The statistical inference of the parameter is studied by considering discrete sampling of the sample paths of the model and then using the maximum likelihood (ML) method. The estimation of the threshold parameter requires the solution of a nonlinear equation. To do so, we propose two methods: the classical Newton–Raphson (NR) method and one based on simulated annealing (SA). This methodology is applied to an example with simulated data corresponding to the process with known parameters. From this, we obtain the estimators of the parameters by both methods (NR and SA). Finally, the methodology studied is applied to a real case concerning the mean age of males in Spain at the date of their first wedding.