Multivariate Time Series Projections of Parameterized Age-Specific Fertility Rates

Abstract

Projection of individual age-specific fertility rates is a forecasting problem of high dimension. We solve this dimensionality problem by using parametric curves to approximate the annual age-specific rates and a multivariate time series model to forecast the curve parameters. These yield forecasts of future fertility curves, which are then used to compute age-specific fertility rate forecasts. This reduces the dimensionality of the forecasting problem and also guarantees that long-run projections of age-specific fertility rates will exhibit a smooth shape across age similar to historical data. Short-term projections are improved by also using simple techniques to forecast the deviations of the fitted curves from the actual rates. The article applies this approach to age-specific fertility data for U.S. white women from 1921–1984. The resulting forecasts are examined, and the multivariate model is used to investigate possible relations between the curve parameters, expressed as the total fertility rate, the mean age of childbearing, and the standard deviation of age at childbearing. The only strong relationship found is the contemporaneous relationship between the mean and standard deviation of age at childbearing. A variation of this approach, in conjunction with traditional demographic judgment, was used in a recent set of U.S. Census Bureau population projections. We discuss this implementation and compare the Census Bureau projections with those produced directly from the model presented here.

Key Words:

• Fertility projection
• Multivariate ARIMA models