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Estimation of Endogenous Volatility Models with Exponential Trends

Author

Listed:
  • Juan R. A. Bobenrieth

    (Departamento of Matemática, Universidad del Bío-Bío, Concepción 4081112, Chile)

  • Eugenio S. A. Bobenrieth

    (Department of Agricultural Economics, Pontificia Universidad Católica de Chile, Santiago 8970117, Chile)

  • Andrés F. Villegas

    (Escuela de Agronomía, Facultad de Recursos Naturales y Medicina Veterinaria, Universidad Santo Tomás, Santiago 8320000, Chile)

  • Brian D. Wright

    (Department of Agricultural and Resource Economics, University of California Berkeley, Berkeley, CA 94720-3310, USA)

Abstract

Nonlinearities, exponential trends, and Euler equations are three key features of standard dynamic volatility models of speculation, economic growth, or macroeconomic fluctuations with occasionally binding constraints and endogenous state-dependent volatility. A natural way to estimate a model with all such three features could be to use the observed nonstationary data in a single step without preliminary linearization, log-linearization, or preliminary detrending. Adoption of this natural strategy confronts a serious challenge that has been neither articulated nor solved: a dichotomy in the empirical model implied by the Euler equation. This leads to a discontinuity in the regression in the limit, rendering the approaches employed in available proofs of consistency inapplicable. We characterize the problem and develop a novel method of proof of consistency and asymptotic normality. Our methodological contribution establishes a foundation for consistent estimation and hypothesis testing of nonstationary models without resorting to preliminary detrending, an a priori assumption that any trend is exactly zero, linearization, or other restrictions on the model.

Suggested Citation

  • Juan R. A. Bobenrieth & Eugenio S. A. Bobenrieth & Andrés F. Villegas & Brian D. Wright, 2022. "Estimation of Endogenous Volatility Models with Exponential Trends," Mathematics, MDPI, vol. 10(15), pages 1-27, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2647-:d:874167
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    References listed on IDEAS

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    1. V., Ernesto Guerra & H., Eugenio Bobenrieth & H., Juan Bobenrieth & Wright, Brian D., 2023. "Endogenous thresholds in energy prices: Modeling and empirical estimation," Energy Economics, Elsevier, vol. 121(C).

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