An analytical formula is derived to approximate the finite sample bias of the ordinary least-squares (OLS) estimator of the autoregressive parameter when the underlying process has a unit root. It is found that the bias is expressible in terms of parabolic cylinder functions which are easy to...

An encompassing formula to calculate density and distribution functions for unit root statistics was given in Abadir (1992, Oxford Bulletin of Economics and Statistics 54, 305-323) and was applied there to computing the exact limiting density and distribution of the Studentized t ratio. That...

Closed forms for the distribution of some conventional statistics are given as a prelude to deriving their asymptotic power functions as unit root tests. In the process, an important distinction is drawn between two classes of statistics: one which relies on deterministic normalizations and the...

A new formula for the mean squared error of a unit root estimator is derived. Its minimization gives rise to an estimator which is almost unbiased, unlike the maximum likelihood estimator. For this reason, it is suggested that the problem of testing for unit roots may be solved more...

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...

The paper by Kiefer, Vogelsang and Bunzel (2000), KVB henceforth, provides an interesting unconventional application of functional limit theory to a conventional problem. In this note, we point out that the limiting distribution of the t^{∗} test proposed by KVB turns out to be equivalent to...

Two problems exist in testing for (co-)integration. One is that current definitions of fractional integration in the time-domain can be incomplete. The other is that disregarding fractional orders of integration can cause incorrectly-sized inference about cointegration. This paper completes the...

The Characteristic Function from a Family of Truncated Normal Distributions -- Solution proposed by Karim Abadir and Tassos Magdalinos. The posers of the problem have raised an important question. We can offer a solution to a more general problem, which covers characteristic functions of...

This note analyzes the recent global recession: its causes, the predictability of the timing of its start and of its end, and the implications for macro policy. These follow from the general-equilibrium macro model of Abadir and Talmain (2002) and its implications for a new type of...

The liquidity patterns of investors provide a new common framework to explain the autocorrelation of returns and volumes, as well as some calendar anomalies. Festivities are occasions around which liquidity constraints are particularly relevant, leading to a quot;festivity effectquot;. This...