Statistical surveillance of cyclical processes with application to turns in business cycles

On-line monitoring of cyclical processes is studied. An important application is early prediction of the next turn in business cycles by an alarm for a turn in a leading index. Three likelihood-based methods for detection of a turn are compared in detail. One of the methods is based on a hidden Markov model. The two others are based on the theory of statistical surveillance. One of these is free from parametric assumptions of the curve. Evaluations are made of the effect of different specifications of the curve and the transitions. 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.