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General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series

TLDR
In this article, a class of model-based filters for extracting trends and cycles in economic time series is presented, which are derived in a mutually consistent manner as the joint solution to a signal extraction problem in an unobserved-components model.

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Another class of Butterworth lters is gven by replacing the sine function in equation (5)
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are most easily linked to unobserved com ponents m odels.
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Citations
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References
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Journal ArticleDOI

Postwar U.S. Business Cycles: An Empirical Investigation

TL;DR: In this article, a procedure for representing a times series as the sum of a smoothly varying trend component and a cyclical component is proposed, and the nature of the comovements of the cyclical components of a variety of macroeconomic time series is documented.
Book

Forecasting, Structural Time Series Models and the Kalman Filter

TL;DR: In this article, the Kalman filter and state space models were used for univariate structural time series models to estimate, predict, and smoothen the univariate time series model.
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Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series

TL;DR: The authors developed a set of approximate band-pass filters and illustrates their application to measuring the business-cycle component of macroeconomic activity, and compared them with several alternative filters commonly used for extracting business cycle components.
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