1 Introduction
2 Forecasting models
2.1 Lee-Carter and augmented common factor models
2.2 2-tier augmented common factor model
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fit \(\widehat{a}_{x,i,j}+\widehat{B}_x \widehat{K}_t\);
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conditional on that, fit \(\widehat{b}_{x,i} \widehat{k}_{t,i}\);
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conditional on the previous two stages, fit \(\widehat{b}_{x,i,j} \widehat{k}_{t,i,j}\).
2.3 2-tier augmented common factor model with cohort extension
3 Comparison of the models
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the 2-tier ACF with a common factor for the total UK population, a gender specific factor, and a gender-country specific factor;
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the 2-tier ACFC model with a gender-specific cohort extension on top of the 2-tier ACF model.
3.1 Model fitting
Fitted model | |||||
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Metrics | Country | Lee-Carter | 1-tier ACF | 2-tier ACF | 2-tier ACFC |
BIC | Overall | 214355 | 216459 | 205253 | 200153 |
AIC | Overall | 202953 | 201786 | 190580 | 183300 |
MAPE | England and Wales (f) | 0.05797 | 0.05787 | 0.05196 | 0.05045 |
Scotland (f) | 0.14843 | 0.14452 | 0.14229 | 0.14060 | |
Northern Ireland (f) | 0.26665 | 0.25882 | 0.26243 | 0.26364 | |
England and Wales (m) | 0.05546 | 0.05387 | 0.04437 | 0.04303 | |
Scotland (m) | 0.12964 | 0.12711 | 0.12945 | 0.12357 | |
Northern Ireland (m) | 0.21604 | 0.20522 | 0.20633 | 0.20672 | |
Overall | 0.14570 | 0.14124 | 0.13872 | 0.13800 | |
ER | England and Wales (f) | 0.96856 | 0.96358 | 0.98057 | 0.99140 |
Scotland (f) | 0.91073 | 0.90641 | 0.91944 | 0.93077 | |
Northern Ireland (f) | 0.85879 | 0.86411 | 0.85709 | 0.86290 | |
England and Wales (m) | 0.98400 | 0.98488 | 0.98914 | 0.99555 | |
Scotland (m) | 0.95979 | 0.96199 | 0.96229 | 0.96797 | |
Northern Ireland (m) | 0.90242 | 0.91782 | 0.91493 | 0.91587 | |
Overall | 0.97839 | 0.97731 | 0.98579 | 0.99369 |