Robust Nonlinear Regression Estimation in Null Recurrent Time Series

Francesco Bravo, Degui Li, Dag Tjostheim

Research output: Contribution to journalArticlepeer-review


In this article, we study parametric robust estimation in nonlinear regression models with regressors generated by a class of non-stationary and null recurrent Markov process. The nonlinear regression functions can be either integrable or asymptotically homogeneous, covering many commonly-used functional forms in parametric nonlinear regression. Under regularity conditions, we derive both the consistency and limit distribution results for the developed general robust estimators (including the nonlinear least squares, least absolute deviation and Huber’s M-estimators). The convergence rates of the estimation depend on not only the functional form of nonlinear regression, but also on the recurrence rate of the Markov process. Some Monte-Carlo simulation studies are conducted to examine the numerical performance of the proposed estimators and verify the established asymptotic properties in finite samples. Finally two empirical applications illustrate the usefulness of the proposed robust estimation method.
Original languageEnglish
Pages (from-to)416-438
Number of pages23
JournalJournal of Econometrics
Issue number2
Early online date4 Dec 2020
Publication statusPublished - 1 Oct 2021

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