Multivariate trend function testing with mixed stationary and integrated disturbances

Trend models are important in describing nonstationary behavior of a time series. In this paper we propose valid tests for the trend coefficients in a multivariate system with mixed stationary, integrated or nearly integrated errors. Cross-sectional and serial dependence in innovations are left unspecified beyond regularity assumptions. We consider two sets of tests based on OLS and SUR estimation of the transformed system. A modified SUR estimator corrected for serial correlation of unknown form is shown to be asymptotically efficient. The standard tests under stationarity are also analyzed and potential misleading inferences are demonstrated. The framework is general allowing for linear and nonlinear trend functions. Asymptotic theory, simulations and an empirical application are provided.