A Time-Frequency Analysis of the Coherences of the US Business

The dating of a possible European business cycle has been inconclusive. At this stage, there is no consensus on the existence of such a cycle, or of its periodicity and amplitude, or of the relationship of individual member countries to that cycle. Yet cyclical convergence is the key consideration for countries that wish to be members of the currency union. The confusion over whether and to what degree the UK is converging on the cycles of her European partners, or whether her cycle is more in line with the US, is an example of this lack of consensus. We show that countries will vary in the components and characteristics that make up their output cycles, as well as in the state of their cycle at any point of time. Next, we show how to decompose a business cycle in a time-frequency framework. This allows us to decompose movements in output, both at the European level and in member countries, into their component cycles and allows those component cycles to vary in importance and cyclical characteristics over time. It also allows us to determine if the inconclusive convergence results so far have appeared because member countries have some cycles in common, but diverge at other frequencies