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Notation and background We propose a new method for robust forecasting of age-specific mortality and fertility rates. To illustrate our methodology, we use annual Australian fertility rates (1921–2000) for five-year age groups The data were obtained from the Australian Bureau of Statistics and are shown as separate time series in Figure 1 (left). We convert(More)
Automatic forecasts of large numbers of univariate time series are often needed in business and other contexts. We describe two automatic forecasting algorithms that have been implemented in the forecast package for R. The first is based on innovations state space models that underly exponential smoothing methods. The second is a step-wise algorithm for(More)
We discuss and compare measures of accuracy of univariate time series forecasts. The methods used in the M-competition and the M3-competition, and many of the measures recommended by previous authors on this topic, are found to be degenerate in commonly occurring situations. Instead, we propose that the mean absolute scaled error become the standard measure(More)
We provide a new approach to automatic forecasting based on an extended range of exponential smoothing methods. Each method in our taxonomy of exponential smoothing methods provides forecasts that are equivalent to forecasts from a state space model. This equivalence allows: (1) easy calculation of the likelihood, the AIC and other model selection criteria;(More)
A new approach is proposed for forecasting a time series with multiple seasonal patterns. A state space model is developed for the series using the innovation approach which enables us to develop explicit models for both additive and multiplicative seasonality. Parameter estimates may be obtained using methods from exponential smoothing. The proposed model(More)
Age-sex-specific population forecasts are derived through stochastic population renewal using forecasts of mortality, fertility and net migration. Functional data models with time series coefficients are used to model age-specific mortality and fertility rates. As detailed migration data are lacking, net migration by age and sex is estimated as the(More)
We compare the short-to medium-term accuracy of five variants or extensions of the Lee-Carter method for mortality forecasting. These include the original Lee-Carter, the Lee-Miller and Booth-Maindonald-Smith variants, and the more flexible Hyndman-Ullah and De Jong-Tickle extensions. These methods are compared by applying them to sex-specific populations(More)
We review the past 25 years of research into time series forecasting. In this silver jubilee issue, we naturally highlight results published in journals managed by the During this period, over one third of all papers published in these journals concerned time series forecasting. We also review highly influential works on time series forecasting that have(More)