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Computation of asymmetric signal extraction filters and mean squared error for ARIMA component models

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  • William R. Bell
  • Donald E. K. Martin
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    Abstract

    Standard signal extraction results for both stationary and nonstationary time series are expressed as linear filters applied to the observed series. Computation of the filter weights, and of the corresponding frequency response function, is relevant for studying properties of the filter and of the resulting signal extraction estimates. Methods for doing such computations for symmetric, doubly infinite filters are well established. This study develops an algorithm for computing filter weights for asymmetric, semi-infinite signal extraction filters, including the important case of the concurrent filter (for signal extraction at the current time point). The setting is where the time series components being estimated follow autoregressive integrated moving-average (ARIMA) models. The algorithm provides expressions for the asymmetric signal extraction filters as rational polynomial functions of the backshift operator. The filter weights are then readily generated by simple expansion of these expressions, and the corresponding frequency response function is directly evaluated. Recursive expressions are also developed that relate the weights for filters that use successively increasing amounts of data. The results for the filter weights are then used to develop methods for computing mean squared error results for the asymmetric signal extraction estimates. Copyright 2004 Blackwell Publishing Ltd.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

    Volume (Year): 25 (2004)
    Issue (Month): 4 (07)
    Pages: 603-623

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    Handle: RePEc:bla:jtsera:v:25:y:2004:i:4:p:603-623

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    Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782

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    Cited by:
    1. Proietti, Tommaso, 2010. "Seasonality, Forecast Extensions and Business Cycle Uncertainty," MPRA Paper 20868, University Library of Munich, Germany.
    2. Balakrishna, N. & Hareesh, G., 2009. "Statistical signal extraction using stable processes," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 851-856, April.
    3. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    4. Maravall, Agustin, 2006. "An application of the TRAMO-SEATS automatic procedure; direct versus indirect adjustment," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2167-2190, May.

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