Detection of Functional Form Misspecification in Cointegrating Relations

Abstract

A simple specification test based on fully modified residuals and the cumulative sum (CUSUM) test for cointegration of Xiao and Phillips (2002, Journal of Econometrics, 108, 43–61) are considered as means of testing for functional form in long-run cointegrating relations. It is shown that both tests are consistent under functional form misspecification and lack of cointegration. A simulation experiment is carried out to assess the properties of the tests in finite samples. The Dickey–Fuller test is also considered. The simulation results reveal that the first two tests perform reasonably well. However, the Dickey–Fuller test performs poorly under functional form misspecification.

Estimation and Inference for Varying-Coefficient Models With Nonstationary Regressors Using Penalized Splines

“…Note that the strong approximation is stronger than the multivariate invariance principle, but it is commonly used in the literature of nonlinear regression model with nonstationary regressors, including Park and Hahn (1999), Park and Phillips (2001), Kasparis (2008), Phillips (2009a, 2009b), Cai et al (2009), Shi andPhillips (2012) among others. Sufficient conditions to derive strong approximations for dependent random variables are also well established in the literature.…”

“…For example, Park and Hahn (1999) construct two residual-based statistics to test the constancy of the cointegrating coefficients based on the series estimation. Kasparis (2008) develops two residual-based statistics for testing the functional form misspecification in cointegrating relations. Bierens and Martins (2010) propose a vector error correction model with cointegration coefficients estimated by Chebyshev polynomials, and conduct a likelihood ratio test on the stability by examining whether all Chebyshev polynomial coefficients are jointly zero.…”

Modelling trends and cycles in economic time series: historical perspective and future developments

“…Examples of this steadily increasing literature are Bec and Rahbek (2004), Kapetanios et al (2006), Kasparis (2008) and Saikkonen (2008). In a similar vein, another interesting area is the analysis of common trends and cointegration within I(2) and fractional I(d) frameworks (for recent research and references, see Nielsen and Rahbek 2007, Hualde and Velasco 2008, and Johansen 2008.…”

The Bierens test for certain nonstationary models

“…It follows from our simulation experiment that all the tests under consideration have reasonable power in the presence of a neglected locally integrable component. Hong and Phillips (2005) and Kasparis (2008) …”