Time series models are often fitted to the data without preliminary checks for stability of the mean and variance, conditions that may not hold in much economic and financial data, particularly over long periods. Ignoring such shifts may result in fitting models with spurious dynamics that lead...

The well-known transformation theorem (or change-of-variables theorem) is difficult to prove, requiring knowledge of theorems in advanced analysis. For this reason, it is stated without proof in all the statistics textbooks we know of. Here, we provide a new and much simpler proof, by exploiting...

It was recently shown (Abadir, K. M. ,1993, On the asymptotic power of unit root tests. Econometric Theory, 9, 189-221) that nonstationarity causes the limiting distributions of the Wald (W) and Lagrange multiplier (LM) statistics to become different from each other. This paper demonstrates that...

A unified framework to derive the distribution of conventional statistics under a unit root is presented. It is based on formulae which can generate (analytically as well as numerically) the densities and distributions of statistics such as the t ratio, the normalized autocorrelation...