Mortality forecasting using factor models: Time-varying or time-invariant factor loadings?

He, Lingyu; Huang, Fei; Shi, Jianjie; Yang, Yanrong

doi:10.1016/j.insmatheco.2021.01.006

Cited by 8 publications

(4 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Log transforms are quite classical in that area of statistical demography (cf. Hyndman and Ullah, 2007;Hyndman and Shang, 2009;He et al, 2021). Gao et al (2019) have also used the log curves for estimating their model but, in the last stage of their forecasting analysis, they compute the exponentials of their forecasted log curves and base their metrics on it.…”

Section: Formentioning

confidence: 99%

Factor models for high‐dimensional functional time series II: Estimation and forecasting

Tavakoli

Nisol

Hallin

2023

Journal Time Series Analysis

View full text Add to dashboard Cite

This article is the second one in a set of two laying the theoretical foundations for a high‐dimensional functional factor model approach in the analysis of large cross‐sections (panels) of functional time series (FTS). Part I establishes a representation result by which, under mild assumptions on the covariance operator of the cross‐section, any FTS admits a canonical representation as the sum of a common and an idiosyncratic component; common components are driven by a finite and typically small number of scalar factors loaded via functional loadings, while idiosyncratic components are only mildly cross‐correlated. Building on that representation result, Part II is dealing with the identification of the number of factors, their estimation, the estimation of their loadings and the common components, and the resulting forecasts. We provide a family of information criteria for identifying the number of factors, and prove their consistency. We provide average error bounds for the estimators of the factors, loadings, and common components; our results encompass the scalar case, for which they reproduce and extend, under weaker conditions, well‐established similar results. Under slightly stronger assumptions, we also provide uniform bounds for the estimators of factors, loadings, and common components, thus extending existing scalar results. Our consistency results in the asymptotic regime where the number of series and the number of time points diverge thus extend to the functional context the ‘blessing of dimensionality’ that explains the success of factor models in the analysis of high‐dimensional (scalar) time series. We provide numerical illustrations that corroborate the convergence rates predicted by the theory, and provide a finer understanding of the interplay between and for estimation purposes. We conclude with an application to forecasting mortality curves, where our approach outperforms existing methods.

show abstract

Section: Formentioning

confidence: 99%

Factor models for high‐dimensional functional time series II: Estimation and forecasting

Tavakoli

Nisol

Hallin

2023

Journal Time Series Analysis

View full text Add to dashboard Cite

show abstract

“…Due to the longevity phenomenon, forecasting mortality has become more and more important for actuaries, pension sponsors and policymakers. Since the seminal work of Lee and Carter (1992), (dynamic) factor models (DFMs), including the Lee-Carter (LC), the Cairns-Blake-Dowd (CBD) models (Cairns et al, 2006) and others (see e.g., French and O'Hare, 2013;Chulia et al, 2016;Heinemann, 2017;Gao et al, 2019;He et al, 2021), have become the workhorse for mortality modelling. 1 Their mathematical simplicity can partly explain this success story since they assume that a small number of factor processes drive age-specific mortality rates.…”

Section: Introductionmentioning

confidence: 99%

Modelling mortality: A bayesian factor-augmented var (favar) approach

Zhu²

2022

ASTIN Bull.

View full text Add to dashboard Cite

Longevity risk is putting more and more financial pressure on governments and pension plans worldwide due to pensioners’ increasing trend of life expectancy and the growing numbers of people reaching retirement age. Lee and Carter (1992, Journal of the American Statistical Association, 87(419), 659–671.) applied a one-factor dynamic factor model to forecast the trend of mortality improvement, and the model has since become the field’s workhorse. It is, however, well known that their model is subject to the limitation of overlooking cross-dependence between different age groups. We introduce Factor-Augmented Vector Autoregressive (FAVAR) models to the mortality modelling literature. The model, obtained by adding an unobserved factor process to a Vector Autoregressive (VAR) process, nests VAR and Lee–Carter models as special cases and inherits both frameworks’ advantages. A Bayesian estimation approach, adapted from the Minnesota prior, is proposed. The empirical application to the US and French mortality data demonstrates our proposed method’s efficacy in both in-sample and out-of-sample performance.

show abstract

“…Please see Renshaw and Haberman (2006) and Cairns et al (2006) for other related seminal work. More recent developments of such models include He et al (2021). Studies such as Perla et al (2021), Richman and Wüthrich (2021), and Wang et al (2021) have considered machine learning extensions of the LC model.…”

Section: Introductionmentioning

confidence: 99%

Forecasting Mortality Rates with a Two-Step LASSO Based Vector Autoregressive Model

Kularatne

Shi

2022

Risks

View full text Add to dashboard Cite

This paper proposes a two-step LASSO based vector autoregressive (2-LVAR) model to forecast mortality rates. Within the VAR framework, recent studies have developed a spatial–temporal autoregressive (STAR) model, in which age-specific mortality rates are related to their own historical values (temporality) and the rates of the neighboring cohorts (spatiality). Despite its desirable age coherence property and the improved forecasting accuracy over the widely used Lee–Carter (LC) model, STAR employs a rather restrictive structure that only allows for non-zero cohort effects of the same cohorts and the neighboring cohorts. To address this limitation, the proposed 2-LVAR model adopts a data-driven principle, as in a sparse VAR (SVAR) model, to offer more flexibility in the parametric structure. A two-step estimation strategy is developed accordingly to resolve the challenging objective function of 2-LVAR, which consists of non-standard L2 and LASSO-type penalties with constraints. Using empirical data from Australia, the United Kingdom, France, and Switzerland, we show that the 2-LVAR model outperforms the LC, STAR, and SVAR models in most of our forecasting results. Further simulation studies confirm this outperformance, and analyses based on life expectancy at birth empirically support the existence of age coherence. The results of this paper will help researchers understand the mortality projections in the long run and improve the reserving/ratemaking accuracy for life insurers.

show abstract

Mortality forecasting using factor models: Time-varying or time-invariant factor loadings?

Cited by 8 publications

References 27 publications

Factor models for high‐dimensional functional time series II: Estimation and forecasting

Factor models for high‐dimensional functional time series II: Estimation and forecasting

Modelling mortality: A bayesian factor-augmented var (favar) approach

Forecasting Mortality Rates with a Two-Step LASSO Based Vector Autoregressive Model

Contact Info

Product

Resources

About