Nonparametric Testing for Linearity in Cointegrated Error-Correction Models

Abstract

The principal objective of this study is to explore nonparametric testing for linearity in the long-run relationship of the cointegrated vector error-correction model. We develop nonparametric tests, which are predicated on general nonlinear specification, and thus nonlinear models such as the smooth transition and threshold cointegration models are contained in our specification. The test statistics can be computed using the null model of standard error correction. The asymptotic distribution of the test statistics is based on the standard distribution, and thus the proposed tests do not involve semiparametric treatment for the resolution of inferential difficulty. The alternative distribution of the test statistics is explored under the local drift and the smooth functional form. The Monte Carlo simulation shows that the proposed tests evidence adequate finite sample performance in detecting omitted nonlinearity. An economic application to the stock price-dividend relation is also provided.