Econometrica: Sep 2008, Volume 76, Issue 5

Testing Models of Low‐Frequency Variability

https://doi.org/10.3982/ECTA6814
p. 979-1016

Ulrich K. Müller, Mark W. Watson

We develop a framework to assess how successfully standard time series models explain low‐frequency variability of a data series. The low‐frequency information is extracted by computing a finite number of weighted averages of the original data, where the weights are low‐frequency trigonometric series. The properties of these weighted averages are then compared to the asymptotic implications of a number of common time series models. We apply the framework to twenty U.S. macroeconomic and financial time series using frequencies lower than the business cycle.
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