### Fathoming the changes to the Lee-Carter model

#### (Feb 19, 2018)

Ancient Greek philosophers had a paradox called "The Ship of Theseus"; if pieces of a ship are replaced over time as they wear out until every one of the original components is gone, is it still the same ship?  At this point you could be forgiven for thinking (a) that this couldn't possibly be further removed from mortality modelling, and (b) that I had consumed something a lot more potent than tea at breakfast.  However, this philosophical parable is relevant to the granddaddy of all stochastic projection models: the one proposed by Lee & Carter (1992).

In their original paper Lee & Carter (1992) proposed the following model:

$\log m_{x,y} = \alpha_x+\beta_x\kappa_y+\epsilon_y$

where $$m_{x,y}$$…

Tags: Lee-Carter, P-splines, ARIMA

### Getting to the root of time-series forecasting

#### (Oct 3, 2016)

When using a stochastic model for mortality forecasting, people can either use penalty functions or time-series methods . Each approach has its pros and cons, but time-series methods are the commonest. I demonstrated in an earlier posting how an ARIMA time-series model can be a better representation of a mortality index than a random walk with drift. In this posting we will examine the structure of an ARIMA model and how one might go around selecting and fitting it.

Assume we have an index at time $$t$$, $$\kappa_t$$, and an error term, $$\epsilon_t$$ ($$\kappa_t$$ could be the mortality index in the Lee-Carter model, for example). For mortality applications the simplest non-trivial forecasting model is the…

#### (Jul 12, 2010)

One of the most written-about models for stochastic mortality projections is that from Lee & Carter (1992).  As Iain described in an earlier post, the genius of the Lee-Carter model lies in reducing a two-dimensional forecasting problem (age and time) to a simpler one-dimensional problem (time only).

A little-appreciated fact is that there are two ways of approaching the time-series projection of future mortality rates.  A simple method is to treat the future mortality index as a simple random walk with drift.  This makes the strong simplifying assumption that the mortality trend changes at a constant rate (apart from the random noise).  Figure 1 shows an example projection for males in England &…