Seasonal patterns in mortality

During an analysis of a large annuity portfolio we took some time out to look at the pattern of mortality by season as well as the overall time trend. We fitted a model for age, gender and season, where the definition of season is that used by the ONS: each season covers three months, and where winter covers December, January and February. The results are shown below, where the mortality index has a value of 100 in January 1998.

Seasonal patterns and time trend for mortality

The chart shows a number of interesting features. Most obviously, there is a strong downward trend, reflecting the ongoing significant improvements in annuitant mortality in the United Kingdom.

The next feature is the strong cyclic intra-year patter: high mortality in winter months, followed by lighter mortality in summer months.

There is also evidence of negative autocorrelation: winters with very heavy mortality tend to be followed by summers with very light mortality. The years 1999 and 2000 show a very wide amplitude due to this.

One conclusion to draw from this is the importance of analysing mortality over as long a time period as possible to reduce the influence of period effects.

Seasonal patterns in Longevitas

Longevitas supports two methods of modelling seasonal patterns:

  1. The CalendarPeriod variable, and
  2. The SeasonalEffect variable.

Longevitas users can fit models with a variety of period effects using the CalendarPeriod variable. Simply go to the Configuration section and enable this in the Modelling tab. There you will also have the option to select the frequency of effects, as well as their alignment during the year. The CalendarPeriod is a categorical variable, i.e. the effect is assumed to be constant within the period.

The SeasonalEffect variable is a feature of the Hermite family of models. It is a continuous variable, and so is a more parsimonious option when modelling post-retirement mortality differentials.

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