Comprehensively testing linearity hypothesis using the smooth transition autoregressive model

This article examines the null limit distribution of quasi-likelihood ratio (QLR) statistic for testing linearity condition against smooth transition autoregressive (STAR) model. We explicitly show that QLR test weakly converges to a functional multivariate Gaussian process under linearity, which is done by resolving issue identification problem arises in two different ways null. In contrast with Lagrange multiplier widely employed condition, proposed has an omnibus power, and thus, it complements existing procedure. empirical relevance our neglected nonlinearity US fiscal multipliers growth rates unemployment. These examples demonstrate useful detecting nonlinear structure among economic variables.