In this thesis, we develope a statistical method to predict the turning points in business cycle. The essence of predicting the turning points in business cycle is that under the assumption of leading composite index``s causal priority to business cycle, if we could detect the changes in leading composite index, then we would predict imminent changes in business cycle.We analyzed the underlying process of leading composite index with the dynamic linear model with random level and random slope where the random slope is distorted by random shock at the turning points. The posterior probability of a significant random shock in the slope component was calculated by Bayesian approach. If this posterior probability would exceed some subjective value, we could predict an imminent turning in business cycle. By the presented model in this thesis the asymmetric behavior of leading composite index over the turning points is well described with the random shock in slope, and the intensity of change is quantified with the estimate of this random shock. In the empirical application to the U.S. leading composite index, we could predict two peaks and three troughs with no false signal and one no signal for three peaks and three troughs after the peak in Nov. 1970. This result was comparable to the best result by the previous studies by Neftci, Chaffin and Talley, and Zarnowitz and Moore.