Inference on a semiparametric model with global power law and local nonparametric trends

This paper studies a model with both a parametric global trend and a nonparametric local trend. This model may be of interest in a number of applications in economics, finance, ecology, and geology. The model nests the parametric global trend model considered in Phillips (2007) and Robinson (2012), and the nonparametric local trend model. We first propose two hypothesis tests to detect whether either of the special cases are appropriate. For the case where both null hypotheses are rejected, we propose an estimation method to capture both aspects of the time trend. We establish consistency and some distribution theory in the presence of a large sample. Moreover, we examine the proposed hypothesis tests and estimation methods through both simulated and real data examples. Finally, we discuss some potential extensions and issues when modelling time effects.