Optimal Linear Filtering, Smoothing and Trend Extraction for m-period Differences of Processes with a Unit Root

Dimitrios Thomakos

No 30, Working Papers from University of Peloponnese, Department of Economics

Abstract: In this paper I consider the problem of optimal linear filtering, smoothing and trend extraction for m-period differences of processes with a unit root. Such processes arise naturally in economics and finance, in the form of rates of change (price inflation, economic growth, financial returns) and finding an appropriate smoother is thus of immediate practical interest. The filter and resulting smoother are based on the methodology of Singular Spectrum Analysis (SSA) and their form and properties are examined in detail. In particular, I find explicit representations for the asymptotic decomposition of the covariance matrix and show that the first two leading eigenvalues of the decomposition account for over 90% of the variability of the process. I examine the structure of the impulse and frequency response functions finding that the optimal filter has a “permanent” and a “transitory component” with the corresponding smoother being the sum of two such components. I also find explicit representations for the extrapolation coefficients that can be used in out-of-sample prediction. The methodology of the paper is illustrated with three short empirical applications using data on U.S. inflation and real GDP growth and data on the Euro/US dollar exchange rate. Finally, the paper contains a new technical result: I derive explicit representations for the filtering weights in the context of SSA for an arbitrary covariance matrix. This result allows one to examine specific effects of smoothing in any situation and has not appeared so far, to the best of my knowledge, in the related literature.

Keywords: core inflation; business cycles; differences; euro; linear filtering; singular spectrum analysis; smoothing; trading strategies; trend extraction and prediction; unit root. (search for similar items in EconPapers)
Pages: 46 pages
Date: 2008
New Economics Papers: this item is included in nep-cba, nep-ecm, nep-ets and nep-mac
References: Add references at CitEc
Citations:

Downloads: (external link)
http://econ.uop.gr/~econ/RePEc/pdf/optimal_smoothing_differences.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 500 Can't connect to econ.uop.gr:80 (A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond.)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:uop:wpaper:0030

Access Statistics for this paper

More papers in Working Papers from University of Peloponnese, Department of Economics Contact information at EDIRC.
Bibliographic data for series maintained by Kleanthis Gatziolis ().