Scoring the composite leading indicators: A Bayesian turning points approach

This paper explores a Bayesian decision-theoretic approach for analysis and development of composite leading indicators. The methods used here are derived from work by Zellner et al. and Zellner and Hong aimed at forecasts time series turning points, and the multi-process mixture models first described by Harrison and Stevens and more recently in West and Harrison. Here, these methods are used to develop composite leading indicators formed by using the posterior probabilities derived from predictive relations between the individual indicator variables and the state of the economy measure as weights. This study, like those of Wecker, Kling and Diebold and Rudebusch, uses the time series observations on the measure of economic activity which it is wished to predict along with an explicit definition of a turning point, either a downturn or upturn. Unlike those studies, a predictive relation is then established between the individual component indicator series and the variable measuring economic activity which allows a Bayesian computation of probabilities associated with the turning point events. This parallels the developments in Zellner et al., where the focus was on forecasting turning points in economic time series. These probabilities are conditioned on the past data and the predictive probability density function for future observations. A composite indicator is devised using a Class I, multi-process mixture model suggested in West and Harrision. The composite indicator arising from this approach is an average of the individual component series, where the averaging is done over the posterior probabilities of the individual component series predictive relations. An example of the procedure is provided using the national composite leading indicator.