Short-term analysis is generally performed with seasonally adjusted data from which further estimation of the business cycle is performed through well-known filters (HP, Baxter-King). However, the whole procedure is not fully consistent, because seasonal adjustment and trend-cycle estimation do not share the same methodological framework, a fact which could potentially entail spurious interpretations. We study this topic from an unified perspective through an extension of Beveridge Nelson decompositions. We show that estimation of the various components of a given time series is feasible once the location of unit roots which drive the persistence of the series have been determined. The precise identification of seasonal unit roots is performed in a preliminary step. Then we derive estimates for each component from a modelization of the raw series which may be parametric (ARMA) or semi parametric, with special attention paid to deterministic components which play a prominent role in the decomposition. Thus, we avoid explicit modelization of each component as required by signal extraction methods or unobserved components analysis. The cycle is simply defined as the stationary stochastic residual of the decomposition. Further properties of this decomposition are investigated in the last part of the paper.
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Paper provided by Banque de France in its series Documents de Travail with number
209.
Find related papers by JEL classification: C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
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