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 lowfrequency signal estimation and interpolation in discrete samples, and examine its properties for simulated series. Illustrations are given on economic data.

中文翻译：

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具有多种采样规则的非平稳时间序列的信号提取

本文提出了一个灵活的框架，用于提取时间序列的信号，这些时间序列是在不同的采样频率下以存量或流量测量的。我们的方法可以对不同采样规则下的序列进行连贯处理，可以更深入地了解信号估计器的主要属性以及测量的作用，还可以采用简单的方法进行信号估计和离散观测的插值。我们提出了重要的理论基础，包括证明了推广到非平稳信号或噪声的连续时间Wiener-Kolmogorov公式的证明。基于这些结果，我们得出了一类新的低通滤波器，它们为库存和流量时间序列的趋势估计提供了基础。此外，我们介绍了一种简单准确的方法，用于离散样本中的低频信号估计和内插，并检查其模拟系列的属性。举例说明了经济数据。