Testing Models of Low-Frequency Variability
We develop a framework to assess how successfully standard times eries 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.
The first draft of this paper was written for the Federal Reserve Bank of Atlanta conference in honor of the twenty-fifth anniversary of the publication of Beveridge and Nelson (1981), and we thank the conference participants for their comments. We also thank Tim Bollerslev, David Dickey, John Geweke and Barbara Rossi for useful comments and discussions, and Rafael Dix Carneiro for excellent research assistance. Support was provided by the National Science Foundation through grants SES-0518036 and SES-0617811. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.