Dynamic Mortality Forecasting via Mixed-Frequency State-Space Models

TL;DR

This paper introduces a mixed-frequency state-space model that combines annual and monthly mortality data to improve real-time mortality forecasting and intra-year nowcasting, leveraging high-frequency death counts.

Contribution

The paper develops a novel mixed-frequency state-space extension of the Lee--Carter model that jointly models annual and monthly mortality data for improved real-time forecasts.

Findings

Aggregated monthly forecasts outperform direct annual forecasts.

Incorporating monthly data improves intra-year nowcasts.

The model produces more cautious predictive intervals than traditional methods.

Abstract

High-frequency death counts are now widely available and contain timely information about intra-year mortality dynamics, but most stochastic mortality models are still estimated on annual data and therefore update only when annual totals are released. We propose a mixed-frequency state-space (MF--SS) extension of the Lee--Carter framework that jointly uses annual mortality rates and monthly death counts. The two series are linked through a shared latent monthly mortality factor, with the annual period factor defined as the intra-year average of the monthly factors. The latent monthly factor follows a seasonal ARIMA process, and parameters are estimated by maximum likelihood using an EM algorithm with Kalman filtering and smoothing. This setup enables real-time intra-year updates of the latent state and forecasts as new monthly observations arrive without re-estimating model parameters. Using U.S. data for ages 20--90 over 1999--2019, we evaluate intra-year annual nowcasts and one- to five-year-ahead forecasts. The MF--SS model produces both a direct annual forecast and an annual forecast implied by aggregating monthly projections. In our application, the aggregated monthly forecast is typically more accurate. Incorporating monthly information substantially improves intra-year annual nowcasts, especially after the first few months of the year. As a benchmark, we also fit separate annual and monthly Lee--Carter models and combine their forecasts using temporal reconciliation. Reconciliation improves these independent forecasts but adds little to MF--SS forecasts, consistent with MF--SS pooling information across frequencies during estimation. The MF--SS aggregated monthly forecasts generally outperform both unreconciled and temporally reconciled Lee--Carter forecasts and produce more cautious predictive intervals than the reconciled Lee--Carter approach.