TRENDS, CYCLES, AND CONVERGENCE

Determining turning points in the business cycle is a difficult problem. Making sensible predictions concerning the growth path of an economy in the medium or long term is even harder. This paper explores what can be achieved by analysing and modeling time se-ries observations on gross domestic product (GDP) and other macro-economic time series. Separating out trends and cycles is fundamental to a good deal of economic analysis. It is often done by applying filters in a rather arbitrary fashion. Thus the low-pass filter introduced by Hodrick and Prescott (1997) is frequently used to remove trends in situa-tions in which it can create serious distortions (see Harvey and Jae-ger, 1993; Cogley and Nason, 1995). The band-pass filter, recently introduced by Baxter and King (1999), can also result in distortions (see Murray, 2002). Trends and cycles are best constructed using unobserved compo-nent, or structural, time series models. The parameters in such mod-els are typically estimated by maximum likelihood, after which op-timal estimates of the components are obtained by smoothing algo-rithms. The calculations are most easily performed by putting the model in state-space form. The paper begins by discussing the basic ideas of structural time series models and reviewing the link with the Hodrick-Prescott (HP) I am grateful to Vasco Carvalho for research assistance, to Rodrigo Caputo and Thomas Trimbur for helpful comments, and to Christian Johnson for his discussion at the conference. Much of the work reported was supported by th