Model Specification Test with Correlated But Not Cointegrated Variables
19 Pages Posted: 27 Aug 2013
Date Written: October 18, 2012
Many macroeconomic and financial variables show highly persistent and correlated patterns but not necessarily cointegrated. Recently, Sun, Hsiao and Li (2010) propose using a semiparametric varying coefficient approach to capture correlations between integrated but non cointegrated variables. Due to the complication arising from the integrated disturbance term and the semiparametric functional form, consistent estimation of such a semiparametric model requires stronger conditions than usually needed for consistent estimation for a linear (spurious) regression model, or a semiparametric varying coefficient model with a stationary disturbance. Therefore, it is important to develop a testing procedure to examine for a given data set, whether linear relationship holds or not, while allowing for the disturbance being an integrated process. In this paper we propose two test statistics for detecting linearity against semiparametric varying coefficient alternative specification. Monte Carlo simulations are used to examine the finite sample performances of the proposed tests.
Keywords: Specification test, Spurious regression, varying coefficient, kernel estimation
JEL Classification: C13, C14, C22
Suggested Citation: Suggested Citation