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

Abstract

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 nonlinear trend present in data corresponding to CO 2 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.

A Stochastic Lomax Diffusion Process: Statistical Inference and Application

“…In this paper we suggest the simulated annealing (SA) method for solving the equations Equations (11) and (12). Hereafter is the description of the method.…”

“…In contrast observations from many fields such a as neuroscience, finance and biology, suggest otherwise. Various non-homogeneous SDPs have been proposed to reflect this time dependent behavior, see for example: Lognormal [9], Gompertz [10], Vasicek [11], Brennan-Schwartz [12], and Gamma [13] processes.…”

“…Simulated sample paths vs. the Estimated Trend Function (ETF) for α = 1.5, β = 90 σ = 0.01.Using the simulated annealing method to solve Equations(11) and (12), we obtained the estimatorsα i ,β i andσ i 2 of each trajectory, and then considered the mean values of the estimators given by α =…”

A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand Dynamics

“…The height-diameter equation or the diameter-height equation can be derived using conditional stationary SDEs. Here, we focus on a multivariate mixed effect parameters hybrid SDE model (Gompertz, Gompertz, and Vasicek, see [17,20,21]),…”

The Stochastic Modified Lundqvist-Korf Diffusion Process: Statistical and Computational Aspects and Application to Modeling of the CO2 Emission in Morocco

“…In this perspective, see, for example, Gutiérrez et al [14] in the study of the SDP with cubic drift with application to a modeling of the global CO 2 emissions in Spain. Then, Gutiérrez et al [13] in the case of the non-homogeneous (with exogenous factors) stochastic Vasicek diffusion process in the case of CO 2 emission in Morocco. Note that the non-homogeneity in this process is obtained by adding exogenous factors such as external variables that affect the drift of the homogeneous Vasicek model.…”