Computation of asymmetric signal extraction filters and mean squared error for ARIMA component models
. 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 th...
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Published in | Journal of time series analysis Vol. 25; no. 4; pp. 603 - 623 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Oxford, UK
Blackwell Publishing Ltd
01.07.2004
Wiley Blackwell |
Series | Journal of Time Series Analysis |
Subjects | |
Online Access | Get full text |
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Summary: | . 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. |
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Bibliography: | ark:/67375/WNG-9CJRNGMS-G istex:D7C0441E923F596D0206074B38A063C52325A4B8 ArticleID:JTSA1920 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0143-9782 1467-9892 |
DOI: | 10.1111/j.1467-9892.2004.01920.x |