Testing of Constant Parameters for Semi-Parametric Functional Coefficient Models with Integrated Covariates

Cointegration has been widely used in macroeconomics and financial time series analysis, but traditional linear cointegration relationship is often rejected in empirical applications. Many constant parameters testing methods in semi-parametric functional coefficient cointegrated framework have been developed accordingly. However, there are little studies on constant parameters testing problem for the case that the index variable is integrated of order one. From a practical point of view, there is also a need for a test that accommodates integrated index variable in functional coefficient cointegrated setting, for example, in the study of the purchasing power parity hypothesis. In this article, an orthogonal series approximation-based test statistic is proposed to tackle the problem. The asymptotic results are also studied. Monte Carlo experiments are conducted to evaluate the finite sample performance of the proposed test, and an empirical example about price and exchange rate data is provided.