Predicting the Turning Points of Business and Economic Time Series

Standard linear least-squares prediction methods are not directly applicable to making probability statements about time series turning points. William F. Wecker suggested a method for extending the least-squares technique to allow computation of the probability distribution of turning points of a time series. Wecker's analysis was univariate and did not consider all sources of uncertainty (i.e., estimates of coefficients). The primary purpose of this paper is fourfold: (1) to extend Wecker's analysis to the case of the multiple time-series model; (2) to consider most sources of model uncertainty; (3) to test the procedure for reliability (method of calibrations); and (4) to demonstrate some interesting applications.