Inference in the Presence of Stochastic and Deterministic Trends

The focus of this paper is inference about stochastic and deterministic trends when both types are present. We show that, contrary to asymptotic theory and the existing literature, the parameters of the deterministic components must be taken into account in finite samples. We analyze the ubiquitous Likelihood Ratio test for the rank of cointegration in vector processes. Here, we directly control the parameters of the data generating process so that a local-asymptotic framework accounts for small sample interactions between stochastic and deterministic trends. We show that the usual corrections are invalid as they take no account of the relative magnitudes of these two types of trends. Block-local models provide an embedding framework which provides a rationale for consistent estimation and testing of the whole set of parameters. In an empirical application to European GDP series, we show that using usual corrections leads to underestimating the number of stochastic trends.