Comprehensive Testing of Linearity against the Smooth Transition Autoregressive Model

Dakyung Seong (), Jin Seo Cho () and Timo Teräsvirta

No 2019rwp-151, Working papers from Yonsei University, Yonsei Economics Research Institute

Abstract: 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 Terasvirta (1994).

Keywords: QLR test statistic; STAR model; linearity test; Gaussian process; null limit distribution; nonstandard testing problem. (search for similar items in EconPapers)
JEL-codes: C12 C18 C46 C52 (search for similar items in EconPapers)
Pages: 44pages
Date: 2019-11
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Working Paper: Comprehensive Testing of Linearity against the Smooth Transition Autoregressive Model (2019)
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