On the Model Based Interpretation of Filters and the Reliability of Trend-Cycle Estimates
Tommaso Proietti
CEIS Research Paper from Tor Vergata University, CEIS
Abstract:
The paper explores and illustrates some of the typical trade-offs which arise in designing filters for the measurement of trends and cycles in economic time series, focusing, in particular, on the fundamental trade-off between the reliability of the estimates and the magnitude of the revisions as new observations become available. This assessment is available through a novel model based approach, according to which an important class of highpass and bandpass filters, encompassing the Hodrick-Prescott filter, are adapted to the particular time series under investigation. Via a suitable decomposition of the innovation process, it is shown that any linear time series with ARIMA representation can be broken down into orthogonal trend and cycle components, for which the class of filters is optimal. The main results then follow from Wiener-Kolmogorov signal extraction theory, whereas exact finite sample inferences are provided by the Kalman filter and smoother for the relevant state space representation of the decomposition.
Keywords: Signal Extraction; Revisions; Kalman filter and Smoother; Bandpass (search for similar items in EconPapers)
Pages: 33
Date: 2006-05-31
New Economics Papers: this item is included in nep-ecm and nep-ets
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https://ceistorvergata.it/RePEc/rpaper/No-84.pdf (application/pdf)
Related works:
Journal Article: On the Model-Based Interpretation of Filters and the Reliability of Trend-Cycle Estimates (2009)
Working Paper: On the Model-Based Interpretation of Filters and the Reliability of Trend-Cycle Estimates (2004)
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Persistent link: https://EconPapers.repec.org/RePEc:rtv:ceisrp:84
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