Forecasting Multiple Functional Time Series in a Group Structure: An Application to Mortality

Abstract

When modeling sub-national mortality rates, we should consider three features: (1) how to incorporate any possible correlation among sub-populations to potentially improve forecast accuracy through multi-population joint modeling; (2) how to reconcile sub-national mortality forecasts so that they aggregate adequately across various levels of a group structure; (3) among the forecast reconciliation methods, how to combine their forecasts to achieve improved forecast accuracy. To address these issues, we introduce an extension of grouped univariate functional time series method. We first consider a multivariate functional time series method to jointly forecast multiple related series. We then evaluate the impact and benefit of using forecast combinations among the forecast reconciliation methods. Using the Japanese regional age-specific mortality rates, we investigate one-step-ahead to 15-step-ahead point and interval forecast accuracies of our proposed extension and make recommendations.

Forecasting Australian subnational age-specific mortality rates

“…This result can be attributed to the MinT method incorporating all information from a full covariance matrix of forecast errors in obtaining a set of coherent forecasts. Both figures also indicate that forecast combination can help reducing point forecast errors, confirming findings of Shang and Hyndman (2017) and Shang and Haberman (2020).…”

“…It is possible to combine the forecast mentioned above reconciliation methods to reduce bias, variance, and uncertainty of forecasts. Shang and Haberman (2020) recently considered a forecast combination method that computes the averaged forecast for horizon h as…”

“…where R g n+h denotes forecasts obtained via a reconciliation method, and w 1 , • • • , w g are weights summing to 1. Following Shang and Haberman (2020), we adopt a simple average combination method that applies equal weighting on the BU, OP and MinT reconciled forecasts as…”

Deep Spatio-Temporal Multiplex Graph Learning for Cardiac Imaging Classification

“…Another point of interest is the generation of the adjacency matrix. It would be interesting to explore the simultaneous learning of the adjacency matrix during task optimization [27] and use the AHA connectivity pattern as prior knowledge to regularize the structural learning. Regarding the temporal aspect, most of the approaches are sequenceto-sequence methods focused on forecast multivariate timeseries.…”

“…Regarding the temporal aspect, most of the approaches are sequenceto-sequence methods focused on forecast multivariate timeseries. These methods are usually based on recurrent neural networks [27], 1D convolutions [28], or transformer-like architectures [29]. Currently, we use the temporal aspect to add a direction in our data and exploit the relative differences between the node states in time.…”