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The exact linkage between the Beveridge–Nelson decomposition and other permanent-transitory decompositions

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  • Sbrana, Giacomo

Abstract

The econometric literature has recently focused attention on the relationship between the Beveridge–Nelson decomposition and unobserved components processes when decomposing time series into permanent and transitory shocks. This paper shows the existence of an algebraic linkage between reduced and structural forms parameters of some unobserved components processes. Results allow measuring how close standard unobserved components processes and unrestricted ARIMA models are regardless of the number of structural/reduced form parameters. Results are provided when the reduced forms are ARIMA(2,1,2) and ARIMA(0,2,2). For the latter, the exact relation between the Hodrick–Prescott filter and the IMA(2,2) reduced form is also shown.

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  • Sbrana, Giacomo, 2013. "The exact linkage between the Beveridge–Nelson decomposition and other permanent-transitory decompositions," Economic Modelling, Elsevier, vol. 30(C), pages 311-316.
    • Handle: RePEc:eee:ecmode:v:30:y:2013:i:c:p:311-316
    DOI: 10.1016/j.econmod.2012.09.039
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    Cited by:

    1. Murasawa, Yasutomo, 2015. "The multivariate Beveridge–Nelson decomposition with I(1) and I(2) series," Economics Letters, Elsevier, vol. 137(C), pages 157-162.
    2. Riccardo De Bonis & Andrea Silvestrini, 2014. "The Italian financial cycle: 1861-2011," Cliometrica, Journal of Historical Economics and Econometric History, Association Française de Cliométrie (AFC), vol. 8(3), pages 301-334, September.

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    More about this item

    Keywords

    Beveridge–Nelson decomposition; Unobserved components processes; Local linear trend; ARIMA;
    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
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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