### 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…