Exploring Excess Death (part 8)

I change tack and explore ARIMA model residuals in time series modelling of ONS all cause weekly registered deaths for 2010 - 2023

An earlier comment by an astute subscriber got me thinking. They wanted to know what the pruned fragments for all cause registered death looked like back in part 3 when glued together as a series. We may think of this as the scraps of pastry that fall to the table as we trim our pie crust.

Whenever we produce a model – ARIMA or otherwise – we always end up with trimmings on the table that we call ‘residuals’ and it occurred to me that a time series of ARIMA model residuals might say something important about what was not expected to happen if death in the UK chugged along as ‘normal’.

To get a goodly amount of pie crust trimming we need to run ARIMA without goodies like indicator variables for pandemic weeks and without outlier detection, but we do need to run it with the seasonal mean serving as an independent variable that stamps out the basic pattern of seasonal variability for all cause death in England & Wales. We also better adopt the seasonal mean series that incorporates the sl…