Working Paper Series no. 209: Short term analysis of raw data and business cycle estimation. Part 1 : estimation and tests. (in French)

Abstract

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.

Renaud Lacroix
April 2008

Classification JEL : C14, C22, E32.

Keywords : Beveridge Nelson decomposition, seasonal unit roots, seasonal adjustment, cycle.