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Signal Extraction for Non‐Stationary Multivariate Time Series with Illustrations for Trend Inflation
Author(s) -
McElroy Tucker,
Trimbur Thomas
Publication year - 2015
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12102
Subject(s) - multivariate statistics , series (stratigraphy) , mathematics , inflation (cosmology) , signal (programming language) , econometrics , sample (material) , order of integration (calculus) , statistics , time series , stationary process , mathematical optimization , computer science , mathematical analysis , paleontology , physics , chemistry , chromatography , theoretical physics , biology , programming language
This article advances the theory and methodology of signal extraction by developing the optimal treatment of difference stationary multivariate time‐series models. Using a flexible time‐series structure that includes co‐integrated processes, we derive and prove formulas for minimum mean square error estimation of signal vectors in multiple series, from both a finite sample and a bi‐infinite sample. As an illustration, we present econometric measures of the trend in total inflation that make optimal use of the signal content in core inflation.