SEMIPARAMETRIC FUNCTIONAL COEFFICIENT MODELS WITH INTEGRATED COVARIATES

Cai, Li, and Park (<italic>Journal of Econometrics</italic>, 2009) and Xiao (<italic>Journal of Econometrics</italic>, 2009) developed asymptotic theories for estimators of semiparametric varying coefficient models when regressors are integrated processes but the smooth coefficients are functionals of stationary processes. Using a recent result from Phillips (<italic>Econometric Theory</italic>, 2009), we extend this line of research by allowing for both the regressors and the covariates entering the smooth functionals to be integrated variables. We derive the asymptotic distribution for the proposed semiparametric estimator. An empirical application is presented to examine the purchasing power parity hypothesis between U.S. and Canadian dollars.