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

Author

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  • Javier Cabello Sánchez

    (Facultad de Ciencias, Universidad de Extremadura, Avda. de Elvas s/n, 06006 Badajoz, Spain
    These authors contributed equally to this work.)

  • Juan Antonio Fernández Torvisco

    (Facultad de Ciencias, Universidad de Extremadura, Avda. de Elvas s/n, 06006 Badajoz, Spain
    These authors contributed equally to this work.)

  • Mariano R. Arias

    (Facultad de Ciencias, Universidad de Extremadura, Avda. de Elvas s/n, 06006 Badajoz, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Javier Cabello Sánchez & Juan Antonio Fernández Torvisco & Mariano R. Arias, 2021. "TAC Method for Fitting Exponential Autoregressive Models and Others: Applications in Economy and Finance," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:862-:d:536071
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    References listed on IDEAS

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    1. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, October.
    2. Harvey J. Greenberg & William P. Pierskalla, 1971. "A Review of Quasi-Convex Functions," Operations Research, INFORMS, vol. 19(7), pages 1553-1570, December.
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    Cited by:

    1. Ionuț Nica & Ștefan Ionescu & Camelia Delcea & Nora Chiriță, 2024. "Quantitative Modeling of Financial Contagion: Unraveling Market Dynamics and Bubble Detection Mechanisms," Risks, MDPI, vol. 12(2), pages 1-42, February.

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