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Nonlinear autoregressive models with optimality properties

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  • Francisco Blasques
  • Siem Jan Koopman
  • André Lucas

Abstract

We introduce a new class of nonlinear autoregressive models from their representation as linear autoregressive models with time-varying coefficients. The parameter updating scheme is subsequently based on the score of the predictive likelihood function at each point in time. We study in detail the information theoretic optimality properties of this updating scheme and establish the asymptotic theory for the maximum likelihood estimator of the static parameters of the model. We compare the dynamic properties of the new model with those of well-known nonlinear dynamic models such as the threshold and smooth transition autoregressive models. Finally, we study the model’s performance in a Monte Carlo study and in an empirical out-of-sample forecasting analysis for U.S. macroeconomic time series.

Suggested Citation

  • Francisco Blasques & Siem Jan Koopman & André Lucas, 2020. "Nonlinear autoregressive models with optimality properties," Econometric Reviews, Taylor & Francis Journals, vol. 39(6), pages 559-578, July.
    • Handle: RePEc:taf:emetrv:v:39:y:2020:i:6:p:559-578
    DOI: 10.1080/07474938.2019.1701807
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    Cited by:

    1. Giacomo Bormetti & Fulvio Corsi, 2021. "A Lucas Critique Compliant SVAR model with Observation-driven Time-varying Parameters," Papers 2107.05263, arXiv.org, revised Feb 2022.
    2. Martí de Castro-Cros & Manel Velasco & Cecilio Angulo, 2021. "Machine-Learning-Based Condition Assessment of Gas Turbines—A Review," Energies, MDPI, vol. 14(24), pages 1-27, December.
    3. Francisco Blasques & Noah Stegehuis, 2024. "A Score-Driven Filter for Causal Regression Models with Time- Varying Parameters and Endogenous Regressors," Tinbergen Institute Discussion Papers 24-016/III, Tinbergen Institute.

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