Integrating uncertainty in time series population forecasts: An illustration using a simple projection model

Abel, Guy J.; Bijak, Jakub; Forster, Jonathan J.; Raymer, James; Smith, Peter; Wong, Jackie S.T.

doi:10.4054/demres.2013.29.43

Cited by 14 publications

(9 citation statements)

References 33 publications

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“…Figure 9 shows the outcomes of the proposed smooth constrained forecasting model. In order to better visualize uncertainty around estimated values, we portray outcomes by means of fanplot (Abel et al 2013). Colored bands are limited by 10% and 90% of the empirical percentiles.…”

Section: Confidence Intervals By Bootstrapmentioning

confidence: 99%

Smooth constrained mortality forecasting

Camarda¹

2019

DemRes

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BACKGROUND Mortality can be forecast by means of parametric models, principal component methods, and smoothing approaches. These methods either impose rigid modeling structures or produce implausible outcomes. OBJECTIVE We propose a novel approach for forecasting mortality that combines a well established smoothing model and prior demographic information. We constrain future smooth mortality patterns to lie within a range of valid age profiles and time trends, both computed from observed patterns. METHODS Within a P-spline framework, we enforce shape constraints through an asymmetric penalty approach on forecast mortality. Moreover, we properly integrate infant mortality in a smoothing framework so that the mortality forecast covers the whole age range. RESULTS The proposed model outperforms the plain smoothing approach as well as commonly used methodologies while retaining all the desirable properties that demographers expect from a forecasting method, e.g., smooth and plausible age profiles and time trends. We illustrate the proposed approach to mortality data for Danish females and US males. CONCLUSIONS The proposed methodology offers a new paradigm in forecasting mortality, and it is an ideal balance between pure statistical methodology and traditional demographic models. Prior knowledge about mortality development can be conveniently included in the approach, leading to large flexibility. The combination of powerful statistical methodology and prior demographic information makes the proposed model suitable for forecasting mortality in most demographic scenarios.

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Section: Confidence Intervals By Bootstrapmentioning

confidence: 99%

Smooth constrained mortality forecasting

Camarda¹

2019

DemRes

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“…Specification of the inherent randomness of the process forms a part of the model design, which can also include additional terms for baseline data errors. The issue of model specification can be addressed by adopting Bayesian model selection and averaging (Raftery 1995 ), as discussed in Section 2 , and this has been done in several demographic applications to estimation (Murphy and Wang 2001 ) and forecasting (Bijak 2010 ; Abel et al 2013a , 2013b ).…”

Section: Key Areas Of Demographic Applicationmentioning

confidence: 99%

“…Recent years have seen several other examples of coherent Bayesian forecasts of whole populations, combining the predictions made for individual demographic components. Abel et al ( 2013b ) have provided a tutorial for overall time series of fertility, mortality, and migration for the United Kingdom, without age (as in Bernardo and Muñoz 1993 ), but with model uncertainty. The model has subsequently been extended by Wis´niowski et al ( 2015 ) to include age by applying a common framework, based on the Lee and Carter ( 1992 ) approach.…”

Section: Key Areas Of Demographic Applicationmentioning

confidence: 99%

Bayesian demography 250 years after Bayes

Bijak

Bryant

2016

Population Studies

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Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250 years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms.

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“…Despite the popularity of model averaging in statistical and forecasting literature (see, e.g., Bates and Granger (1969); Dickinson (1975); Clemen (1989)), model averaging has not received increasing attention in the demographic literature with the noticeable exceptions of Shang (2012); Shang (2015) in the context of mortality forecasting, ((Bijak 2011), Chapter 5) in the context of migration forecasting, and Abel et al (2013) and Shang et al (2014) for the overall population growth rate. Shang (2012) revisited many statistical methods and combined their forecasts based on two weighting schemes, one of which has been adapted for comparison in the “A competing model averaging method” section.…”

Section: Introductionmentioning

confidence: 99%

Model confidence sets and forecast combination: an application to age-specific mortality

Shang

Haberman

2018

Genus

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BackgroundModel averaging combines forecasts obtained from a range of models, and it often produces more accurate forecasts than a forecast from a single model.ObjectiveThe crucial part of forecast accuracy improvement in using the model averaging lies in the determination of optimal weights from a finite sample. If the weights are selected sub-optimally, this can affect the accuracy of the model-averaged forecasts. Instead of choosing the optimal weights, we consider trimming a set of models before equally averaging forecasts from the selected superior models. Motivated by Hansen et al. (Econometrica 79(2):453–497, 2011), we apply and evaluate the model confidence set procedure when combining mortality forecasts.Data and methodsThe proposed model averaging procedure is motivated by Samuels and Sekkel (International Journal of Forecasting 33(1):48–60, 2017) based on the concept of model confidence sets as proposed by Hansen et al. (Econometrica 79(2):453–497, 2011) that incorporates the statistical significance of the forecasting performance. As the model confidence level increases, the set of superior models generally decreases. The proposed model averaging procedure is demonstrated via national and sub-national Japanese mortality for retirement ages between 60 and 100+.ResultsIllustrated by national and sub-national Japanese mortality for ages between 60 and 100+, the proposed model-averaged procedure gives the smallest interval forecast errors, especially for males.ConclusionWe find that robust out-of-sample point and interval forecasts may be obtained from the trimming method. By robust, we mean robustness against model misspecification.Electronic supplementary materialThe online version of this article (10.1186/s41118-018-0043-9) contains supplementary material, which is available to authorized users.

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Integrating uncertainty in time series population forecasts: An illustration using a simple projection model

Cited by 14 publications

References 33 publications

Smooth constrained mortality forecasting

Smooth constrained mortality forecasting

Bayesian demography 250 years after Bayes

Model confidence sets and forecast combination: an application to age-specific mortality

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