A permanent-transitory decomposition for ARFIMA processes. (English) Zbl 1094.62108

Summary: The purpose of this paper is to present a decomposition into a trend or permanent component and a cycle or transitory component of a time series that follows a nonstationary \((d > {1}/{2})\) autoregressive fractionally integrated moving average ARFIMA(\(p,d,q\)) model. The decomposition depends only on past data and is thus computable in real time. We also provide an algorithm for the efficient and exact computation of the decomposition. The empirical applicability of our decomposition is illustrated with a study of German unemployment rate series.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P20 Applications of statistics to economics
65C60 Computational problems in statistics (MSC2010)
91B40 Labor market, contracts (MSC2010)


Full Text: DOI


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