Comprehensive Testing of Linearity against the Smooth Transition Autoregressive Model

Publikation: Working paperForskning


  • rp19_17

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  • Dakyung Seong, University of California Davis, USA
  • Jin Seo Cho, Yonsei University, Sydkorea
  • Timo Teräsvirta
This paper examines the null limit distribution of the quasi-likelihood ratio (QLR) statistic that tests linearity condition using the smooth transition autoregressive (STAR) model. We explicitly show that the QLR test statistic weakly converges to a functional of a Gaussian stochastic process under the null of linearity by resolving the issue of twofold identification meaning that Davies’s (1977, 1987) identification problem arises in two different ways under the null. We illustrate our theory using the exponential STAR and logistic STAR models and also conduct Monte Carlo simulations. Finally, we test for neglected nonlinearity in the German money demand, growth rates of US unemployment, and German industrial production. These empirical examples also demonstrate that the QLR test statistic complements the linearity test of the Lagrange multiplier test statistic in Teräsvirta (1994).
UdgiverInstitut for Økonomi, Aarhus Universitet
Antal sider44
StatusUdgivet - 1 nov. 2019
SerietitelCREATES Research Papers


  • QLR test statistic, STAR model, Linearity test, Gaussian process, Null limit distribution, Nonstandard testing problem

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