On the Model Based Interpretation of Filters and the Reliability of Trend-Cycle Estimates

35 Pages Posted: 31 May 2006

See all articles by Tommaso Proietti

Tommaso Proietti

University of Rome II - Department of Economics and Finance

Date Written: May 2006

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

Suggested Citation

Proietti, Tommaso, On the Model Based Interpretation of Filters and the Reliability of Trend-Cycle Estimates (May 2006). CEIS Working Paper No. 84. Available at SSRN: https://ssrn.com/abstract=905289 or http://dx.doi.org/10.2139/ssrn.905289

Tommaso Proietti (Contact Author)

University of Rome II - Department of Economics and Finance ( email )

Via Columbia, 2
Rome, 00133
Italy

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
101
Abstract Views
840
rank
273,608
PlumX Metrics