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Interpretation of the Effects of Filtering Integrated Time Series

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  • João Valle e Azevedo

Abstract

We resort to a rigorous definition of spectrum of an integrated time series in order to characterise the implications of applying linear filters to such series. We conclude that in the presence of integrated series the transfer function of the filters has exactly the same interpretation as in the covariance stationary case, contrary to what many authors suggest. This disagreement leads to different conclusions regarding the link of the original fluctuations with the transformed fluctuations in the time series data, embodied in various unjustified criticisms to the application of detrending filters. Despite this, and given the frequency domain characteristics of filtered macroeconomic integrated series, we acknowledge that the choice of a particular detrending filter is far from being a neutral task.

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  • João Valle e Azevedo, 2007. "Interpretation of the Effects of Filtering Integrated Time Series," Working Papers w200712, Banco de Portugal, Economics and Research Department.
    • Handle: RePEc:ptu:wpaper:w200712
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    Cited by:

    1. Andrle, Michal, 2008. "The Role of Trends and Detrending in DSGE Models," MPRA Paper 13289, University Library of Munich, Germany.

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    More about this item

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • 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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