TAC Method for Fitting Exponential Autoregressive Models and Others: Applications in Economy and Finance

Javier Cabello Sánchez, Juan Antonio Fernández Torvisco and Mariano R. Arias
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Javier Cabello Sánchez: Facultad de Ciencias, Universidad de Extremadura, Avda. de Elvas s/n, 06006 Badajoz, Spain
Juan Antonio Fernández Torvisco: Facultad de Ciencias, Universidad de Extremadura, Avda. de Elvas s/n, 06006 Badajoz, Spain
Mariano R. Arias: Facultad de Ciencias, Universidad de Extremadura, Avda. de Elvas s/n, 06006 Badajoz, Spain

Mathematics, 2021, vol. 9, issue 8, 1-20

Abstract: There are a couple of purposes in this paper: to study a problem of approximation with exponential functions and to show its relevance for economic science. The solution of the first problem is as conclusive as it can be: working with the max-norm, we determine which datasets have best approximation by means of exponentials of the form f ( t ) = b + a exp ( k t ) , we give a necessary and sufficient condition for some a , b , k ? R to be the coefficients that give the best approximation, and we give a best approximation by means of limits of exponentials when the dataset cannot be best approximated by an exponential. For the usual case, we have also been able to approximate the coefficients of the best approximation. As for the second purpose, we show how to approximate the coefficients of exponential models in economic science (this is only applying the R-package nlstac ) and also the use of exponential autoregressive models, another well-established model in economic science, by utilizing the same tools: a numerical algorithm for fitting exponential patterns without initial guess designed by the authors and implemented in nlstac . We check one more time the robustness of this algorithm by successfully applying it to two very distant areas of economy: demand curves and nonlinear time series. This shows the utility of TAC (Spanish for CT scan) and highlights to what extent this algorithm can be useful.

Keywords: autoregressive; exponential decay; exponential fitting; approximation; infinity norm; TAC; nlstac (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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