General and Consistent Signal Extraction for Nonstationary Time Series with Diverse Sampling Rules

• Activity Number: 119
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Thomas Trimbur*+ and Tucker S. McElroy
• Companies: Federal Reserve Board and U.S. Census Bureau
• Keywords: Band Pass Filters ; Continuous Time Models ; Hodrick-Prescott Filter ; Turning points ; Trends

Abstract

This paper presents a new framework for flexible signal extraction from time series measured as stock or flow or by another related convention. Our approach allows for a coherent treatment of series across diverse sampling rules, a deeper understanding of the main properties of signal estimators and the role of measurement, and a straightforward method for signal estimation and interpolation for discrete observations. We set out the essential theoretical foundations, including a proof of the continuous-time Wiener-Kolmogorov formula generalized to nonstationary signal or noise, which is crucial for the analysis of economic time series, and. Based on these results, we present a new class of low-pass filters that provide the basis for trend estimation of stock and flow time series. Further, we introduce a simple and accurate method for low-frequency signal estimation and interpolation in discrete samples, and examine its properties for simulated series. Illustrations are given for time series of US inflation.