Comprehensively testing linearity hypothesis using the smooth transition autoregressive model
研究了准似然比统计量在检验线性假设时的极限分布，证明其具有全局检验力，并通过美国财政乘数和失业率增长率的实证展示了其检测非线性结构的能力。
This article examines the null limit distribution of the quasi-likelihood ratio (QLR) statistic for testing linearity condition against the smooth transition autoregressive (STAR) model. We explicitly show that the QLR test statistic weakly converges to a functional of a multivariate Gaussian process under the null of linearity, which is done by resolving the issue of identification problem arises in two different ways under the null. In contrast with the Lagrange multiplier test that is widely employed for testing the linearity condition, the proposed QLR statistic has an omnibus power, and thus, it complements the existing testing procedure. We show the empirical relevance of our test by testing the neglected nonlinearity of the US fiscal multipliers and growth rates of US unemployment. These empirical examples demonstrate that the QLR test is useful for detecting the nonlinear structure among economic variables.