Improved frequency selective filters
Computational Statistics & Data Analysis - Special issue: Computational econometrics
New algorithms for dating the business cycle
Computational Statistics & Data Analysis
An application of the TRAMO-SEATS automatic procedure; direct versus indirect adjustment
Computational Statistics & Data Analysis
Econometric methods of signal extraction
Computational Statistics & Data Analysis
Editorial: 2nd Special Issue on Statistical Signal Extraction and Filtering
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
International Journal of Remote Sensing
Trend filtering via empirical mode decompositions
Computational Statistics & Data Analysis
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The time aggregation properties of the Hodrick-Prescott (HP) filter, which decomposes a time series into trend and cycle, are analyzed for the case of annual, quarterly, and monthly data. Aggregation of the disaggregate components cannot be obtained as the exact result from direct application of an HP filter to the aggregate series. Employing several criteria, HP decompositions for different levels of aggregation that provide similar results can be found. The aggregation is guided by the principle that the period associated with the frequency for which the filter gain is 12 should not be altered. This criterion is intuitive and easy to apply. It is shown that it is approximated, to the first order, by an already proposed empirical rule and that alternative, more complex criteria yield similar results. Moreover, the values of the smoothing parameter of the HP filter that provide results which are approximately consistent under aggregation are considerably robust with respect to the ARIMA model of the series. Aggregation is found to perform better for the case of temporal aggregation than for systematic sampling. The desirability of exact aggregation consistency is investigated. A clarification concerning the supposed spuriousness of the cycles obtained by the HP filter is discussed.