In this paper we build a unifying framework under which the time‐domain properties of the permanent‐transitory decompositions available in the literature are investigated. Starting from the state space representation of a cointegrated system expressions are derived for the (common) trends and cycles of the Beveridge–Nelson decomposition involving quantities already available from the interim multiplier representation. The cycles result from both movements along the attractor and adjustment dynamics; the latter are shown to be the transitory component of the Gonzalo–Granger decomposition. The two decompositions are equivalent when the number of common cycles and trends add up to the dimension of the system. Algorithms for the extraction of the components are given and the results are illustrated with respect to a trivariate system consisting of US per capita GNP, Private Consumption and Investment.

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This paper proposes a dating algorithm based on an appropriately defined Markov chain that enforces alternation of peaks and troughs, and duration constraints concerning the phases and the full cycle. The algorithm, which implements Harding and Pagan's non-parametric dating methodology, allows an assessment of the uncertainty of the estimated turning points caused by filtering and can be used to construct indices of business cycle diffusion, aiming at assessing how widespread are cyclical movements throughout the economy. Its adaptation to the notion of a deviation cycle and the imposition of depth constraints are also discussed. We illustrate the algorithm with reference to the issue of dating the euro-area business cycle and analysing its characteristics, both from the classical and the growth cycle perspectives.

The paper advocates the use of state space methods to deal with the problem of temporal disaggregation by dynamic regression models, which encompass the most popular techniques for the distribution of economic flow variables, such as Chow-Lin, Fernandez and Litterman. The state space methodology offers the generality that is required to address a variety of inferential issues that have not been dealt with previously. The paper contributes to the available literature in three ways: (i) it concentrates on the exact initialization of the different models, showing that this issue is of fundamental importance for the properties of the maximum likelihood estimates and for deriving encompassing autoregressive distributed lag models that nest exactly the traditional disaggregation models; (ii) it points out the role of diagnostics and revisions histories in judging the quality of the disaggregated estimates and (iii) it provides a thorough treatment of the Litterman model, explaining the difficulties commonly encountered in practice when estimating this model. Copyright Royal Economic Society 2006