On the Statistical Properties of a Simple Index of Persistence : Theory and Empirical Applications

The issue of estimating the persistence of a dynamic process arises frequently in many micro and macro applied exercises. In this note we study the statistical properties of a simple index of persistence. We show that the index is normally-distributed and we estimate its expected value and standard deviations under different benchmark null hypotheses for the underlying data-generating mechanisms. Finally, we present a macroeconomic application to exemplify how to statistically discriminate between high and low levels of the index according to the maintained null hypothesis