Forecasting mortality rates: multivariate or univariate models?

2021

Risks

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This paper proposes an age-coherent sparse Vector Autoregression mortality model, which combines the appealing features of existing VAR-based mortality models, to forecast future mortality rates. In particular, the proposed model utilizes a data-driven method to determine the autoregressive coefficient matrix, and then employs a rotation algorithm in the projection phase to generate age-coherent mortality forecasts. In the estimation phase, the age-specific mortality improvement rates are fitted to a VAR model with dimension reduction algorithms such as the elastic net. In the projection phase, the projected mortality improvement rates are assumed to follow a short-term fluctuation component and a long-term force of decay, and will eventually converge to an age-invariant mean in expectation. The age-invariance of the long-term mean guarantees age-coherent mortality projections. The proposed model is generalized to multi-population context in a computationally efficient manner. Using single-age, uni-sex mortality data of the UK and France, we show that the proposed model is able to generate more reasonable long-term projections, as well as more accurate short-term out-of-sample forecasts than popular existing mortality models under various settings. Therefore, the proposed model is expected to be an appealing alternative to existing mortality models in insurance and demographic analyses.

Section: The Two-population Extensionmentioning

confidence: 99%

Mortality Forecasting with an Age-Coherent Sparse VAR Model

2021

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“…Nevertheless, ETS models with seasonal components are not applicable to our study because seasonality is not present in mortality forecasting. In addition, Feng and Shi (2018) suggest that only 2 A maximum likelihood method may also be employed to calibrate the parameters (Renshaw and Haberman 2003).…”

Section: Exponential Smoothing State Space (Ets) Modelmentioning

confidence: 99%

“…Although the LC model receives criticisms for its insufficient allowance for potential volatility in mortality forecasts (see, for example, Wong et al 2020), it has been regarded as a benchmark in various studies. For instance, Feng and Shi (2018) adopt the exponential smoothing state space (ETS) model 1 to predict mortality rates and compare its performance with those under the LC, functional data model (FDM) as well as some univariate time series processes. Thereinto, the ETS model turns out to be the best-performing choice based on Australian population data.…”

Section: Introductionmentioning

confidence: 99%

A Two-Population Extension of the Exponential Smoothing State Space Model with a Smoothing Penalisation Scheme

Tang

2020

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The joint modelling of mortality rates for multiple populations has gained increasing popularity in areas such as government planning and insurance pricing. Sub-groups of a population often preserve similar mortality features with short-term deviations from the common trend. Recent studies indicate that the exponential smoothing state space (ETS) model can produce outstanding prediction performance, while it fails to guarantee the consistency across neighbouring ages. Apart from that, single-population models such as the famous Lee-Carter (LC) may produce divergent forecasts between different populations in the long run and thus lack the property of the so-called coherence. This study extends the original ETS model to a two-population version (2-ETS) and imposes a smoothing penalisation scheme to reduce inconsistency of forecasts across adjacent ages. The exponential smoothing parameters in the 2-ETS model are fitted by a Fourier functional form to reduce dimensionality and thus improve estimation efficiency. We evaluate the performance of the proposed model via an empirical study using Australian female and male population data. Our results demonstrate the superiority of the 2-ETS model over the LC and ETS as well as two multi-population methods - the augmented common factor model (LL) and coherent functional data model (CFDM) regarding forecast accuracy and coherence.

“…To further examine the forecasting effectiveness of the ASTAR model shown above, we follow Feng and Shi (2018) and perform simulation studies in this section. For all five countries, we generate 1,000 replicates.…”

Section: Empirical Applicationmentioning

confidence: 99%

“…This has spurred serious concerns regarding the corresponding mortality and longevity risks. Mortality (longevity) risk describes the fact that people are surviving shorter (longer) than expected (Feng & Shi, 2018); For instance, advances in medical science, technological improvements, and lifestyle changes may very likely result in greater mortality improvements, thus increasing the exposure to longevity risk. For demographic research, accurate mortality forecasting is critical to practices such as population projection.…”

Section: Introductionmentioning

confidence: 99%

Forecasting mortality rates with the adaptive spatial temporal autoregressive model

2020

Journal of Forecasting

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Accurate forecasts of mortality rates are essential to various types of demographic research such as population projection, and the pricing of insurance products such as pensions and annuities. Recent studies have considered a spatial temporal autoregressive (STAR) model for the mortality surface, where mortality rates for each age depend (temporally) on their historical values as well as (spatiality) on those of neighboring age cohorts. This model has sound statistical properties including cointegrated dependent variables and the existence of closed-form solutions. Despite its improved forecasting performance over the famous Lee-Carter (LC) model, the constraint that only the effects of the same and neighboring cohorts are significant can be too restrictive. In this study, we adopt a data-driven adaptive weighted structure and propose the adaptive STAR (ASTAR) model. Retaining all the desirable features of the STAR, our model uniformly outperforms the LC and STAR counterparts in terms of forecasting accuracy, when mortality data for ages 0-100 from the UK, France, Italy, Spain, and Japan over the period 1950-2016 are considered.Two sensitivity tests and additional simulation results also lead to robust conclusions. The proposed ASTAR model could therefore be a widely useful tool for modeling and forecasting mortality rates in other contexts, and may be extended to multipopulation modeling.