Signal Extraction for Nonstationary Multivariate Time Series with Illustrations for Trend Inflation

45 Pages Posted: 20 Dec 2012

See all articles by Tucker McElroy

Tucker McElroy

U.S. Census Bureau - Center for Statistical Research and Methodology

Thomas M. Trimbur

University of Cambridge - Faculty of Economics and Politics

Date Written: May 22, 2012

Abstract

This paper advances the theory and methodology of signal extraction by introducing asymptotic and finite sample formulas for optimal estimators of signals in nonstationary multivariate time series. Previous literature has considered only univariate or stationary models. However, in current practice and research, econometricians, macroeconomists, and policy-makers often combine related series -- that may have stochastic trends -- to attain more informed assessments of basic signals like underlying inflation and business cycle components. Here, we use a very general model structure, of widespread relevance for time series econometrics, including flexible kinds of nonstationarity and correlation patterns and specific relationships like cointegration and other common factor forms. First, we develop and prove the generalization of the well-known Wiener-Kolmogorov formula that maps signal-noise dynamics into optimal estimators for bi-infinite series. Second, this paper gives the first explicit treatment of finite-length multivariate time series, providing a new method for computing signal vectors at any time point, unrelated to Kalman filter techniques; this opens the door to systematic study of near end-point estimators/filters, by revealing how they jointly depend on a function of signal location and parameters. As an illustration we present econometric measures of the trend in total inflation that make optimal use of the signal content in core inflation.

Keywords: co-integration, common trends, filters, multivariate models, stochastic trends, unobserved components

JEL Classification: C32

Suggested Citation

McElroy, Tucker and Trimbur, Thomas M., Signal Extraction for Nonstationary Multivariate Time Series with Illustrations for Trend Inflation (May 22, 2012). FEDS Working Paper No. 2012-45, Available at SSRN: https://ssrn.com/abstract=2191272 or http://dx.doi.org/10.2139/ssrn.2191272

Tucker McElroy (Contact Author)

U.S. Census Bureau - Center for Statistical Research and Methodology ( email )

4600 Silver Hill Road
Washington, DC 20233-9100
United States

Thomas M. Trimbur

University of Cambridge - Faculty of Economics and Politics ( email )

Austin Robinson Building
Sidgwick Avenue
Cambridge, CB3 9DD
United Kingdom

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