Nonlinear autoregressive models with optimality properties

Francisco Blasques; Siem Jan Koopman; André Lucas

doi:10.1080/07474938.2019.1701807

Nonlinear autoregressive models with optimality properties

Francisco Blasques, Siem Jan Koopman^*, André Lucas

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	559-578
Number of pages	20
Journal	Econometric Reviews
Volume	39
Issue number	6
Early online date	31 Dec 2019
DOIs	https://doi.org/10.1080/07474938.2019.1701807
Publication status	Published - 2 Jul 2020

Funding

Blasques and Lucas thank the Dutch National Science Foundation (NWO; grant VICI453-09-005) for financial support. Koopman acknowledges support from CREATES, Aarhus University, Denmark; it is funded by Danish National Research Foundation, (DNRF78). We thank Howell Tong and Timo Ter?svirta for helpful comments and suggestions.

Keywords

Macroeconomic time series
Score driven time-varying parameter models
Smooth transition
Treshold autoregressive models

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AB - 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.

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Nonlinear autoregressive models with optimality properties

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