Methods for continuously monitoring business cycles are compared. A turn in a leading index can be used to predict a turn in the business cycle. 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 a parametric likelihood ratio method. Another includes a non-parametric estimation procedure. The third is based on a Hidden Markov Model. Evaluations are made of several features such as knowledge of shape and parameters of the curve, types and probabilities of transitions and smoothing. Results on the expected delay time [of](to) a correct alarm and the predictive value of an alarm are discussed...