Testing For and Dating Common Breaks in Multivariate Time Series

Abstract

This paper develops methods for constructing asymptotically valid confidence intervals for the date of a single break in multivariate time series, including Z(O), Z(l), and deterministically trending regressors. Although the width of the asymptotic confidence interval does not decrease as the sample size increases, it is inversely related to the number of series which have a common break date, so there are substantial gains to multivariate inference about break dates. These methods are applied to two empirical examples: the mean growth rate of output in three European countries, and the mean growth rate of U.S. consumption, investment, and output.

Is fuel-switching a no-regrets environmental policy? VAR evidence on carbon dioxide emissions, energy consumption and economic performance in Portugal

“…The long-term refers to the time horizon over which the growth effects of the innovations disappear, i.e., the accumulated impulse-response functions converge. The accumulated elasticities, therefore, represent the long-term accumulated percentage point changes in the different variables for one long-term 5 The possible zero effects of innovations in gas and biomass on employment are irrelevant for our results and conclusions since they only reflect the indirect effects of these forms of energy on output. The total effects on output are unambiguously positive as displayed in the bottom panels of Figures 4 and 6.…”

“…Indeed, it is important to highlight that our estimates for the effect of innovations in coal demand show a confidence interval that reinforces the very small impact it has on the economy and does unquestionably include zero effects. 5 …”

How strong is the linkage between tourism and economic growth in Europe?

“…In fact, to motivate the rolling window spillovers analysis below, we have tested for structural breaks in the VAR equations for each country, based on the approach developed by Bai et al (1998). According to this approach, the maximum Wald statistic and the logarithm of the Andrews-Ploberger exponential Wald statistic are used to test the null hypothesis of no common break in the variables (in our case, tourism and economic growth) in the VAR.…”

A Small-Sample Study of the New-Keynesian Macro Model

“…We select our sample period based on the sup-Wald statistic for parameter instability, derived by Bai, Lumsdaine, and Stock (1998). This statistic detects the most likely date for a break in all the parameters of a reduced form VAR.…”