The paper analyzes the impact of the initial observation on the problem of testing for unit roots. To this end, we derive a family of optimal tests that maximize a weighted average power criterion with respect to the initial observation. We then investigate the relationship of this optimal...

The paper investigates inference in nonlinear and non-Gaussian models with moderately time varying parameters. We show that for many decision problems, the sample information about the parameter path can be summarized by an artificial linear and Gaussian model, at least asymptotically. The...

The paper considers time series GMM models where a subset of the parameters are time varying. We focus on an empirically relevant case with moderately large instabilities, which are well approximated by a local asymptotic embedding that does not allow the instability to be detected with...

We develop a general approach to robust inference about a scalar parameter when the data is potentially heterogeneous and correlated in a largely unknown way. The key ingredient is the following result of Bakirov and Sz´ekely (2005) concerning the small sample properties of the standard t-test:...

Tests for stationarity are routinely applied to highly persistent time series. Following Kwiatkowski, Phillips, Schmidt and Shin (1992), standard stationarity tests employ a rescaling by an estimator of the long-run variance of the (potentially) stationary series. This paper analytically...

There are a large number of tests for instability or breaks in coefficients in regression models designed for different possible departures from a stable regression. We make two contributions to this literature. First, we provide conditions under which optimal tests are asymptotically...