Trend–Cycle Decompositions with Correlated Components

This paper raises some interpretative issues that arise from univariate trend–cycle decompositions with correlated disturbances. In particular, it discusses whether the interpretation of a negative correlation as providing evidence for the prominence of real, or supply, shocks, can be supported.

For this purpose it determines the conditions under which correlated components may originate from the underestimation of the cyclical component in an orthogonal decomposition; from the presence of a growth rate cycle, rather than a deviation cycle; or alternatively, as a consequence of the hysteresis phenomenon. Finally, it considers interpreting correlated components in terms of permanent–transitory decompositions, where the permanent component has richer dynamics than a pure random walk.

The consequences for smoothing and signal extraction are discussed: in particular, it is documented that a negative correlation implies that future observations carry most of the information needed to assess cyclical stance. As a result, the components will be subject to underestimation in real time and thus to high revisions. The overall conclusion is that the characterization of economic fluctuations in macroeconomic time series largely remains an open issue.

Keywords:

• Hysteresis
• Permanent–transitory decomposition
• Revisions
• Signal extraction

Mathematics Subject Classification:

• 62P20
• 62M10
• 62M20
• 60G35
• 93E14
• 93E11
• 91B84

ACKNOWLEDGMENTS

I am grateful to an anonymous referee for insightful comments.