This paper considers estimation based on a set of <italic>T</italic> + 1 discrete observations, <italic>y</italic>(0), <italic>y</italic>(<italic>h</italic>), <italic>y</italic>(2<italic>h</italic>),…, <italic>y</italic>(<italic>Th</italic>) = <italic>y</italic>(<italic>N</italic>), where <italic>h</italic> is the sampling frequency and <italic>N</italic> is the span of the data. In contrast to the standard approach of driving <italic>N</italic> to infinity for a fixed sampling frequency, the current paper...

This paper considers the distribution of the Dickey-Fuller test in a model with non-zero initial value and drift and trend. We show how stochastic integral representations for the limiting distribution can be derived either from the local to unity approach with local drift and trend or from the...