Abstract
Abstract This paper presents a flexible framework for signal extraction of time series measured as stock or flow at diverse sampling frequencies. 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. Based on these results, we derive 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 on economic data.
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