Arima models of seasonal variation in U. S. birth and death rates

Abstract This paper applies methods of seasonal ARIMA time series analysis to U. S. monthly birth and death rates for January 1950–December 1978. For model selection, the conventional Box-Jenkins (1970, 1976) diagnostic checks are used in conjunction with some suggestions of Nerlove et al. (1979). This results in final models that contain significant second-order autoregressive components, as well as seasonal moving-average components, for both series. In addition, some evidence is found in the birth rate series for weekly periodicities. These findings imply the existence of a seasonal adjustment procedure that improves on the Census X-11 program currently used by vital statistics agencies.