Signal extraction for nonstationary multivariate time series with illustrations for trend inflation
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2012-45.
Date of creation: 2012
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-14 (All new papers)
- NEP-ECM-2012-07-14 (Econometrics)
- NEP-ETS-2012-07-14 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Durbin, James & Koopman, Siem Jan, 2001.
"Time Series Analysis by State Space Methods,"
Oxford University Press, number 9780198523543.
- Tom Doan, . "SEASONALDLM: RATS procedure to create the matrices for the seasonal component of a DLM," Statistical Software Components RTS00251, Boston College Department of Economics.
- Nyblom, Jukka & Harvey, Andrew, 1999.
"Tests of Common Stochastic Trends,"
Cambridge Working Papers in Economics
9902, Faculty of Economics, University of Cambridge.
- Trimbur, Thomas M., 2010. "Stochastic level shifts and outliers and the dynamics of oil price movements," International Journal of Forecasting, Elsevier, vol. 26(1), pages 162-179, January.
- McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(04), pages 988-1009, August.
- Neil Shephard & Jurgen Doornik & Siem Jan Koopman, 1998.
"Statistical algorithms for models in state space using SsfPack 2.2,"
Economics Series Working Papers
1998-W06, University of Oxford, Department of Economics.
- Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
- Koopman, S.J.M. & Shephard, N. & Doornik, J.A., 1998. "Statistical Algorithms for Models in State Space Using SsfPack 2.2," Discussion Paper 1998-141, Tilburg University, Center for Economic Research.
- Arabinda Basistha & Richard Startz, 2008. "Measuring the NAIRU with Reduced Uncertainty: A Multiple-Indicator Common-Cycle Approach," The Review of Economics and Statistics, MIT Press, vol. 90(4), pages 805-811, November.
- Michael T. Kiley, 2008. "Estimating the common trend rate of inflation for consumer prices and consumer prices excluding food and energy prices," Finance and Economics Discussion Series 2008-38, Board of Governors of the Federal Reserve System (U.S.).
- Valle e Azevedo, Joao & Koopman, Siem Jan & Rua, Antonio, 2006. "Tracking the Business Cycle of the Euro Area: A Multivariate Model-Based Bandpass Filter," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 278-290, July.
- Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
- McElroy, Tucker & Sutcliffe, Andrew, 2006. "An iterated parametric approach to nonstationary signal extraction," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2206-2231, May.
- Tucker McElroy & Michael W. McCracken, 2012. "Multi-step ahead forecasting of vector time series," Working Papers 2012-060, Federal Reserve Bank of St. Louis.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Kris Vajs).
If references are entirely missing, you can add them using this form.