Optimal Linear Filtering, Smoothing and Trend Extraction for Processes with Unit Roots and Cointegration

43 Pages Posted: 27 Mar 2008 Last revised: 14 Jun 2008

See all articles by Dimitrios D. Thomakos

Dimitrios D. Thomakos

University of Peloponnese - School of Management, Economics and Informatics; University of Bologna - Rimini Center for Economic Analysis (RCEA)

Date Written: June 9, 2008

Abstract

In this paper I propose a novel optimal linear filter for smoothing, trend and signal extraction for time series with a unit root. The filter is based on the Singular Spectrum Analysis (SSA) methodology, takes the form of a particular moving average and is different from other linear filters that have been used in the existing literature. To best of my knowledge this is the first time that moving average smoothing is given an optimality justification for use with unit root processes. The frequency response function of the filter is examined and a new method for selecting the degree of smoothing is suggested. I also show that the filter can be used for successfully extracting a unit root signal from stationary noise. The proposed methodology can be extended to also deal with two cointegrated series and I show how to estimate the cointegrating coefficient using SSA and how to extract the common stochastic trend component. A simulation study explores some of the characteristics of the filter for signal extraction, trend prediction and cointegration estimation for univariate and bivariate series. The practical usefulness of the method is illustrated using data for the US real GDP and two financial time series.

Keywords: cointegration, forecasting, linear filtering, singular spectrum analysis, smoothing, trend extraction and prediction, unit root

JEL Classification: C13, C14, C22, C32, C53

Suggested Citation

Thomakos, Dimitrios D., Optimal Linear Filtering, Smoothing and Trend Extraction for Processes with Unit Roots and Cointegration (June 9, 2008). Available at SSRN: https://ssrn.com/abstract=1113331 or http://dx.doi.org/10.2139/ssrn.1113331

Dimitrios D. Thomakos (Contact Author)

University of Peloponnese - School of Management, Economics and Informatics ( email )

Department of Economics
22100 Tripolis
Greece
+30 2710 230139 (Fax)

HOME PAGE: http://es.uop.gr/

University of Bologna - Rimini Center for Economic Analysis (RCEA)

Via Patara, 3
Rimini (RN), RN 47900
Italy

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