Neighbouring Prediction for Mortality

In this study, we propose a nonlinear Bayesian extension of the Lee–Carter (LC) model using a single-stage procedure with a dimensionality reduction neural network (NN). LC is originally estimated using a two-stage procedure: dimensionality reduction of data by singular value decomposition followed by a time series model fitting. To address the limitations of LC, which are attributed to the two-stage estimation and insufficient model fitness to data, single-stage procedures using the Bayesian state-space (BSS) approaches and extensions of flexibility in modeling by NNs have been proposed. As a fusion of these two approaches, we propose a NN extension of LC with a variational autoencoder that performs the variational Bayesian estimation of a state-space model and dimensionality reduction by autoencoding. Despite being a NN model that performs single-stage estimation of parameters, our model has excellent interpretability and the ability to forecast with confidence intervals, as with the BSS models, without using Markov chain Monte Carlo methods.

Section: Extensions Of Lcmentioning

confidence: 99%

Extending the Lee–carter Model With Variational Autoencoder: A Fusion of Neural Network and Bayesian Approach

Miyata

Matsuyama²

2022

“…Thereby, the model can incorporate the correlation structure of mortality rates along the age dimension as well as a variety of age-year interaction effects. These are generally referred to as neighborhood effects by Wang et al (2021), who provide some further motivation for the approach. Similar ideas have been investigated in the mortality modeling literature based on classical time series analysis, for example, by Denton et al (2005), who find that correlations between the residuals of their ARIMA mortality models for adjacent age groups tend to be high.…”

Section: Convolutional Neural Networkmentioning

confidence: 99%

“…This is in line with the approach of Meier and Wüthrich (2020), who use two-dimensional CNN for detecting anomalies in mortality data. Wang et al (2021) consider CNN with two-dimensional convolutions as well and show that they produce more accurate one-step point forecasts than classical stochastic mortality models.…”

mentioning

confidence: 99%

Point and Interval Forecasts of Death Rates Using Neural Networks

Schnürch

Korn

2021

The Lee–Carter model has become a benchmark in stochastic mortality modeling. However, its forecasting performance can be significantly improved upon by modern machine learning techniques. We propose a convolutional neural network (NN) architecture for mortality rate forecasting, empirically compare this model as well as other NN models to the Lee–Carter model and find that lower forecast errors are achievable for many countries in the Human Mortality Database. We provide details on the errors and forecasts of our model to make it more understandable and, thus, more trustworthy. As NN by default only yield point estimates, previous works applying them to mortality modeling have not investigated prediction uncertainty. We address this gap in the literature by implementing a bootstrapping-based technique and demonstrate that it yields highly reliable prediction intervals for our NN model.

“…Perla et al (2021) further extended the model of Richman and Wüthrich (2021) by introducing RNNs and convolutional neural networks (CNNs), specifically designed to model sequential data such as time-series data. The use of convolutional networks for mortality modelling was also investigated in Wang et al (2020). Despite the models proposed in Richman and Wüthrich (2021) and Perla et al (2021) present more accurate forecasts than the ILC approach, how to forecast uncertainty can be derived remains an open issue.…”

Section: Introductionmentioning

confidence: 99%

Calibrating the Lee-Carter and the Poisson Lee-Carter Models via Neural Networks

Scognamiglio

2022

This paper introduces a neural network (NN) approach for fitting the Lee-Carter (LC) and the Poisson Lee-Carter model on multiple populations. We develop some NNs that replicate the structure of the individual LC models and allow their joint fitting by simultaneously analysing the mortality data of all the considered populations. The NN architecture is specifically designed to calibrate each individual model using all available information instead of using a population-specific subset of data as in the traditional estimation schemes. A large set of numerical experiments performed on all the countries of the Human Mortality Database shows the effectiveness of our approach. In particular, the resulting parameter estimates appear smooth and less sensitive to the random fluctuations often present in the mortality rates’ data, especially for low-population countries. In addition, the forecasting performance results significantly improved as well.