Robust forecasting of mortality and fertility rates: A functional data approach

By Rob J Hyndman, Md. Shahid Ullah. Computational Statistics & Data Analysis, 2007

723 citations recorded by the source corpus.

A new method is proposed for forecasting age-specific mortality and fertility rates observed over time. This approach allows for smooth functions of age, is robust for outlying years due to wars and epidemics, and provides a modelling framework that is easily adapted to allow for constraints and other information. Ideas from functional data analysis, nonparametric smoothing and robust statistics are combined to form a methodology that is widely applicable to any functional time series data observed discretely and possibly with error. The model is a generalization of the Lee-Carter (LC) model commonly used in mortality and fertility forecasting. The methodology is applied to French mortality data and Australian fertility data, and the forecasts obtained are shown to be superior to those from the LC method and several of its variants.

Subfields: Demography, Economics and Econometrics, General Health Professions

View Paper: https://www.semanticscholar.org/paper/4089f23172d168edb87eea0a2478564039da5e8a

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Citations in the corpus

Robust functional principal components: A projection-pursuit approach (2011, methodology): “The spherical principal components, noted in the Introduction, which were proposed by Locantore et al. (1999) and further developed by Gervini (2008), apply this approach using the spatial covariance operator.”
Smoothing and projecting age-specific probabilities of death by TOPALS (2012, neutral): “Note that several authors suggest to smooth the mortality rates or the age-specific components of the Lee-Carter model to obtain smooth projections (e.g., Renshaw and Haberman, 2003; Hyndman and Ullah, 2007).”
A survey of functional principal component analysis (2014, methodology): “The observed log mortality rates were smoothed using penalized splines with the partial monotonic constraint , as described in Ramsay ( 1988 ) and Hyndman & Ullah ( 2007 ) .”
Rainbow Plots, Bagplots, and Boxplots for Functional Data (2010, methodology): “The data were taken from the Human Mortality Database (2008), and smoothed using penalized splines as described in Hyndman & Ullah (2007).”
Stochastic population forecasts using functional data models for mortality, fertility and migration (2008, methodology): “Hyndman and Ullah (2007) applied a similar method as part of a functional data approach, and this method is further developed in this paper.”
Functional clustering and linear regression for peak load forecasting (2010, methodology): “Hyndman and Ullah (2007) propose a robust methodology for forecasting functional time series; their original method, which is applied in the demographic context in particular, also differs from our approach in that they forecast a smoothed function instead of a scalar, as in our problem.”
Forecasting: theory and practice (2020, methodology): “, 2010), and functional data model (Hyndman and Ullah, 2007), as well as their extensions and generalisations are dominant.”
Locally Stationary Functional Time Series (2016, background): “In demography, mortality and fertility rates are given as a function of age (e.g. Erbas, Hyndman and Gertig, 2007; Hyndman and Ullah, 2007; Hyndman and Booth, 2008), while in geophysical sciences, magnometers record the strength and direction of the magnetic field every five seconds.”
Applications of functional data analysis: A systematic review (2013, methodology): “Although some authors believe that FDA can be considered as a smoothed version of multivariate data analysis, recent work has shown the advantage of direct application of smoothing techniques to reduce some of the inherent randomness in the observed data [1,25,113].”
Modelling function‐valued stochastic processes, with applications to fertility dynamics (2017, background): “Similarly, Hyndman and Ullah (2007) and Hyndman and Shang (2009) considered functional time series in a setting where only one realization is observed.”
Mortality Modelling and Forecasting: a Review of Methods (2008, methodology): “Hyndman & Ullah (2007) developed an approach based on the functional data paradigm in which data are smoothed across age prior to modelling using penalised regression splines.”
Dynamic functional principal components (2012, methodology): “[9], Reiss and Ogden [33]) or forecasting (Hyndman and Ullah [20], Aue et al.”