Signal Extraction for Nonstationary Multivariate Time Series with Illustrations for Trend Inflation
45 Pages Posted: 20 Dec 2012
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: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Measuring the NAIRU with Reduced Uncertainty: A Multiple Indicator-Common Component Approach
By Arabinda Basistha and Richard Startz
-
In Search of the Natural Rate of Unemployment
By Thomas B. King and James Morley
-
The Clark Model with Correlated Components
By Kum Hwa Oh and Eric Zivot
-
Capacity Utilisation, Constraints and Price Adjustments Under the Microscope
By Sarah M. Lein and Eva M. Kberl
-
Output Fluctuations in the G-7: An Unobserved Components Approach
By Sinchan Mitra and Tara M. Sinclair
-
Testing Stationarity with Unobserved Components Models
By James Morley, Irina Panovska, ...
-
A Review of Cyclical Indicators for the United States: Preliminary Results
-
Demand Variability, Supply Shocks and the Output-Inflation Tradeoff
By Richard T. Froyen and Roger N. Waud