Nonlinear autoregressive models with optimality properties

Francisco Blasques, Siem Jan Koopman*, André Lucas

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


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 languageEnglish
Pages (from-to)559-578
Number of pages20
JournalEconometric Reviews
Issue number6
Early online date31 Dec 2019
Publication statusPublished - 2 Jul 2020


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


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