The purpose of this paper is to construct a leading index for the United States by deriving a set of weights based on Kalman filters. The weights have certain optimality properties and are related to the existing weighting methods of A. F. Burns and W. C. Mitchell (1946), S. H. Hymans (1973), and A. J. Auerbach (1982). The Kalman filter leading index is compared with the CIBCR leading composite index and an index suggested by Auerbach by subjecting all indexes to a number of tests. The results of the tests are mixed, but suggest that the use of Kalman filters as a way of constructing leading indexes is encouraging.

Recently developed methods in the analysis and measurement of latent factor models for time series are utilised to study international business cycles and their relationship to international stockmarket price behaviour. An advantage of these methods is that the duality properties between time domain and frequency domain approaches for investigating the properties of time series can be exploited to identify and model business cycles. The empirical results show that the six countries studied, which include the United States, Australia, Canada, United Kingdom, Germany and Japan, exhibit coherent national business cycles, although these cycles are not all alike. It is also found that international coherence in economic activity has increased in the flexible exchange rate period, although it is not as strong as it is for the national business cycles. The coherence between stockmarket prices and business cycles is not strong, both nationally and internationally, but international stockmarkets appear to show greater mutual coherence than do the corresponding economies.