Likelihood based methods for detection of turning points in business cycles - A comparative study

Abstract

Methods for on-line monitoring of business cycles are compared with respect to the ability of early prediction of the next tum by an alarm for a tum in a leading index. Three likelihood-based methods for turning point detection are compared in detail by using the theory of statistical surveillance and by simulations. One of the methods is based on a Hidden Markov Model. Another includes a non-parametric estimation procedure. Evaluations are made of several features such as knowledge of shape and parameters of the curve, types and probabilities of transitions and smoothing. The methods are made comparable by alarm limits, which give the same median time to the first false alarm, but also other approaches for comparability are discussed. Results are given on the expected delay time to a correct alarm, the probability of detection of a turning point within a specified time and the predictive value of an alarm. The three methods are also used to analyze an actual data set of a period of the Swedish industrial production. The relative merits of evaluation of methods by one real data set or by simulations are discussed.