Greenhouse Emission Forecast as an Inverse Stochastic Problem: A Cross-Entropy Econometrics Approach

Abstract

This paper proposes the non-extensive entropy econometric approach to predict regional cross-industry greenhouse emissions within a country, based on imperfect knowledge of industrial and regional aggregates. The solution of this stochastic inverse problem is applied to Poland. Non-extensive entropy should remain a valuable device for econometric modelling even in the case of low frequency series since outputs provided by the Gibbs-Shannon entropy approach correspond to the Tsallis entropy limiting case of the Gaussian law when the Tsallis q-parameter equals unity. We, therefore, set up a q-Tsallis-Kullback-Leibler entropy criterion function with a priori consistency constraints, including the environmental Kuznets econometric model and regular conditions. As in the case of Shannon-Gibbs-based entropy models, we found that the Tsallis entropy estimator also belongs to the family of Stein estimators, meaning that smaller probabilities are shrunk and higher probabilities dominate in the solution space. Fortunately, adding more pertinent data to the model priors will enhance parameter precision and then allow for the recovery of the real influence of smaller events. The q-Tsallis-Kullback-Leibler entropy index is computed for different scenarios of the Kuznets model. The model outputs continue to conform to empirical expectations. In spite of the close to unity q-Tsallis parameter, this Tsallis related approach reflects higher stability for parameter computation in comparison with the Shannon-Gibbs entropy econometrics technique.

Non-Extensive Entropy Econometrics for Low Frequency Series

“…An inverse problem (e.g., Thikonov et al (1977), Bwanakare (2015), ) explains a situation where one tries to capture the causes of phenomena for which experimental observations represent the effect.…”

“…where p km is the probability of outcome v km and the probabilities must be non-negative and sum up to one. Similarly, by treating each element e i of e as a finite and discrete 34 Reparametrization aims at treating parameters of the model as outputs of probability distribution to be estimated following the procedure presented by and later exploited for modelling many entropy econometric models (see, e.g., Bwanakare et al ( , 2015Bwanakare et al ( , 2016. Since the same probabilities are related to entropy variable defining the criterion function, optimizing the whole model then leads to outputs taking into account stochastic a priori information owing to model restrictions.…”

Wykorzystanie Statystycznych I Pozastatystycznych (Big Data) Źródeł Informacji Do Wyznaczania Kierunków Rozwoju Miast Na Przykładzie Rzeszowa

“…Metoda ta wywodzi się z fizyki, ale zyskuje uznanie w naukach społecznych. Więcej o metodzie i jej zastosowaniach można znaleźć w następujących opracowaniach [1,2,3]. Szczegółowej analizie poddano punkty pomiarowe położone wzdłuż dróg wyjazdowych z Rzeszowa.…”

Predicting Gross Domestic Product Components through Tsallis Entropy Econometrics

“…This is a basic model which consists of solving an integral equation of the first kind. Following [12], inverse problem recovery finds application in various fields of science, particularly in context of optimal control theory. Among different techniques proposed for solving this type of problems, the Tikhonov related regularization theory [13] remains the most applied, besides the Gibbs-Shannon-Jaynes (e.g.…”