Separating cyclical movement from trend growth at seasonal and business cycle frequencies is important to macroeconomic research. At business cycle frequencies, time trends, first differences and the more recent Hodrick-Prescott (HP) filter are used to separate trends from cycles. At seasonal frequencies, ad-hoc methods like the Census Bureau’s X-11 seasonal filter are applied. This paper revie...

Acknowledgments I acknowledge useful conversations with Serena Ng, James Stock, and Vince Wiggins. The KPSS code was adapted from John Barkoulas’ RATS code for that test. Thanks also to Richard Sperling for tracking down a discrepancy between published work and the dfgls output and alerting me to the Cheung and Lai estimates. Any remaining errors are my own. References Cheung, Y. W. and K.-S. L...

The asymptotic behavior of the Granger-causality test under stochastic nonstationarity is studied. Our results confirm that the inference drawn from the test is not reliable when the series are integrated to the first order. In the presence of deterministic components, the test statistic diverges, eventually rejecting the null hypothesis, even when the series are independent of each other. More...

Two approaches have dominated formulations designed to capture small departures from unit root autoregressions. The first involves deterministic departures that include local-to-unity (LUR) and mildly (or moderately) integrated (MI) specifications where departures shrink to zero as the sample size n → ∞. The second approach allows for stochastic departures from unity, leading to stochastic unit...

Linear filters used in seasonal adjustment (model-based or from the X-11 method) contain unit root factors in the form of differencing operators and seasonal summation operators. The extent to which the various filters (seasonal, seasonal adjustment, trend, and irregular) contain these unit root factors determines whether the filters reproduce or annihilate (i) fixed seasonal effects, and (ii) ...

Unit-root testing strategies are unnecessarily complicated because they do not exploit prior knowledge of the growth status of the time series, they worry about unrealistic outcomes, and they doubleor triple-test for unit roots. The authors provide a testing strategy that cuts through these complications and so facilitates teaching this dimension of the unit-root phenomenon. F tests are used as...

This special issue deals with problems related to unit roots and structural change, and the interplay between the two. The research agenda dealing with these topics have proven to be of importance for devising procedures that are reliable for inference and forecasting. Several important contributions have been made. Still, there is scope for improvements and analyses of the properties of existi...

In this paper we propose a generalised autoregressive conditional heteroskedasticity (GARCH) model-based test for a unit root. The model allows for two endogenous structural breaks. We test for unit roots in 156 US stocks listed on the NYSE over the period 1980 to 2007. We find that the unit root null hypothesis is rejected in 40% of the stocks, and only in four out of the nine sectors the null...

Received wisdom: industrial-country floating exchange rates contain unit roots. In three types of tests, however, the data support nominal-rate mean reversion. First, SUR tests on panels of Group-of-Ten nominal rates frequently reject the null of unit roots in favor of mean reversion for various samples over the current float, the first such results in the literature. Second, in out-of-sample f...