Modelling monthly birth and deaths using Seasonal Forecasting Methods as an input for population estimates

The Labour Force Survey (LFS) collects information on a sample population and, every calendar quarter, needs advanced data on estimates of resident population for each NUTS 3. In Portugal, the LFS quarter results are published around forty days after the end of the survey period. This calendar is incompatible with the current production of population estimates, since data on the three components – births, deaths and migration – are not yet available. As such, monthly forecasts of live 42 The 18th ASMDA International Conference (ASMDA 2019) births, deaths and migration must be used. Empirical time series data for births and deaths by NUTS 3 in Portugal shows strong evidence of the presence of seasonality patterns, which mean that appropriate forecasting methods must be considered. In this paper we address the problem of forecasting monthly live births and deaths by NUTS 3 and sex and the distribution of the total predicted deaths by age. The purpose is to use seasonal forecasting methods in order to capture the seasonal behavior of the data. First, for each individual time series graphical analysis is used to analyze past behaviour of fertility and mortality. Second, three alternative methodologies are considered to model and forecast the number of births and deaths by NUTS 3 and sex: ARIMA models with a seasonal component, Holt-Winters exponential smoothing models, and state-space models. Multiple combinations of each of the three alternative types of models are used to fit births and deaths for each NUTS 3, and the best model is chosen using the BIC criterion. To evaluate the forecasting power of each model we use a back-testing procedure using various summary measures of the deviation between the observed values and the forecast point estimates. To assess the robustness of the empirical results to changes in the observation period, we conduct a
sensitivity test on the forecasting power of each model considering a longer observation period and a more recent one. The methodology that provides the best forecasting performance for the majority of the NUTS 3 is adopted. Given the forecasted total number of monthly deaths for each NUTS 3, we use a cohort component approach to distribute deaths by individual age considering the most up-to-date death probabilities derived from complete life tables and a calibration procedure to redistribute the residual component.