New algorithms for dating the business cycle
A new strategy for dating the business cycle turning points, both in the classical and the deviation sense, is presented. After reviewing the available solutions, and in particular the popular Bry and Boschan routine, the role of filtering operations in the preliminary identification of candidate turning points is discussed. Low-pass filters are employed to reduce the amplitude of those fluctuations with period less than the minimum cycle duration. Secondly, the alternation of phases and minimum duration ties are enforced by a dating algorithm based on a Markov chain. Final turning points are identified on the original series by a constrained search around the preliminary points. Dating the deviation cycle poses similar problems, but it requires band pass filters or cyclical models. Applications are presented that illustrate the assessment of the uncertainty surrounding the identified turning points and the construction of a diffusion index from a multivariate time series.
markov chains signal extraction band-pass filters simulation smoothing coincident indicators