Maravall and del Río (2001), analized the time aggregation properties of the Hodrick-Prescott (HP) filter, which decomposes a time series into trend and cycle, for the case of annual, quarterly, and monthly data, and showed that aggregation of the disaggregate component cannot be obtained as the exact result from direct application of an HP filter to the aggregate series. The present paper show...

This paper describes a framework of how to optimally implement linear filters for finite time series. The filters under consideration have the property that they minimize the mean squared error compared to some ideal hypothetical filter. It is shown in examples that three commonly used filters, the bandpass filter, the Hodrick-Prescott filter and the digital Butterworth filter need to be adjust...

In this paper, we investigate eligibility of trend extraction through the empirical mode decomposition (EMD) and performance improvement of applying the ensemble EMD (EEMD) instead of the EMD for trend extraction from seasonal time series. The proposed method is an approach that can be applied on any time series with any time scales fluctuations. In order to evaluate our algorithm, experimental...

Author Contact: David E. Giles, Dept. of Economics, University of Victoria, P.O. Box 1700, STN CSC, Victoria, B.C., Canada V8W 2Y2; e-mail: [email protected]; Phone: (250) 721-8540; FAX: (250) 721-6214 Abstract By noting that the Hodrick-Prescott filter can be expressed as the solution to a particular regression problem, we are able to show how to construct confidence bands for the filtered time-s...

The decomposition and filtering of time series is an important issue in economics and econometrics and related fields. Even though there are numerous competing methods on the market, in application one often meets one of the few favorites. The first method to mention in this selection is the so called Hodrick & Prescott (1997)-filter (HP-filter hereafter). The idea is to decompose a time series...