Runze Li, Rui Zhou, David Pitt
arXiv 9 Jan 2026 · Econometrics
arXiv:2601.05702 · PDF · DOI · OpenAlex · Extracted main text
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.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | George Athanasopoulos and Rob J. Hyndman and Nikolaos Kourentzes and… (2017) Forecasting with temporal hierarchies | 0.874 | 5 | 2 | 100% |
| 2 | Lee, R. and Carter, L (1992) Modeling and forecasting U. S. mortality | 0.843 | 3 | 3 | 100% |
| 3 | Rob J. Hyndman and Roman A. Ahmed and George Athanasopoulos and Han… (2011) Optimal combination forecasts for hierarchical time series | 0.811 | 4 | 2 | 100% |
| 4 | Durbin, James and Koopman, Siem Jan (2012) Time Series Analysis by State Space Methods | 0.737 | 3 | 3 | 67% |
| 5 | Kalman, R. E (1960) A New Approach to Linear Filtering and Prediction Problems | 0.737 | 3 | 2 | 100% |
| 6 | Fung, Man Chung and Peters, Gareth W. and Shevchenko, Pavel V (2017) A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecast… | 0.644 | 2 | 2 | 100% |
| 7 | Fung, Man Chung and Peters, Gareth W. and Shevchenko, Pavel V (2019) Cohort effects in mortality modelling: a Bayesian state-space approach | 0.644 | 2 | 2 | 100% |
| 8 | Fung, Man Chung and Peters, Gareth W. and Shevchenko, Pavel V (2015) A State-Space Estimation of the Lee-Carter Mortality Model and Implications for Annuity Pricing | 0.644 | 2 | 2 | 100% |
| 9 | Pedroza, Claudia (2006) A Bayesian forecasting model: predicting U.S. male mortality | 0.644 | 2 | 2 | 100% |
| 10 | D. M. Dunn and W. H. Williams and T. L. Dechaine (1976) Aggregate versus Subaggregate Models in Local Area Forecasting | 0.511 | 2 | 1 | 100% |
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