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Trend estimation, signal-noise ratios and the frequency of observations

Author

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  • Andrew Harvey

Abstract

The implied signal extraction filters in unobserved components models depend on key signal-noise ratios. This paper examines how these ratios change with the observation interval. The analysis is based on continuous time models and is carried out for both stocks and flows. As a by-product, a connection is established between continuous time flow models and the canonical decomposition. The implications of using the Hodrick-Prescott filter to extract cycles at annual and monthly frequencies are discussed. Many of the arguments used in the literature to set the smoothing constant are shown to be flawed. The analysis suggests that a model-based approach is the best way to proceed. A model formulated in continuous time, or in discrete time at a fine time interval, automatically adapts to any observation interval if it is set up in state space form. Concerns about the change in the shape of the filter and the way in which the signal-noise ratio adapts are then no longer an issue

Suggested Citation

  • Andrew Harvey, 2004. "Trend estimation, signal-noise ratios and the frequency of observations," Econometric Society 2004 Australasian Meetings 343, Econometric Society.
    • Handle: RePEc:ecm:ausm04:343
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    Citations

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    Cited by:

    1. Alessandra Iacobucci & Alain Noullez, 2005. "A Frequency Selective Filter for Short-Length Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 75-102, February.
    2. Tucker S. McElroy & Thomas M. Trimbur, 2007. "Continuous time extraction of a nonstationary signal with illustrations in continuous low-pass and band-pass filtering," Finance and Economics Discussion Series 2007-68, Board of Governors of the Federal Reserve System (U.S.).

    More about this item

    Keywords

    Butterworth filter; Canonical decomposition; Continuous time model; Hodrick-Prescott filter; State space; Unobserved components;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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