This note introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite sample bias, are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and...

Speculative bubbles have played an important role ever since in financial economics. During an ongoing bubble it is relevant for investors and policy-makers to know whether the bubble continues to grow or whether it is already collapsing. Prices are typically well approximated by a random walk...