# Information Matrix

## Filter Information matrix

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### Robust mortality forecasting for 2D age-period models

The covid-19 pandemic caused mortality shocks in many countries, and these shocks severely impact the standard forecasting models used by actuaries. I previously showed how to robustify time-series models with a univariate index (Lee-Carter, APC) and those with a multivariate index (Cairns-Blake-Dowd, Tang-Li

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: outliers, Filter information matrix by tag: coronavirus, Filter information matrix by tag: forecasting, Filter information matrix by tag: mortality projections

### Forecasting with penalty functions - Part III

This is the last of my three blogs on forecasting with penalties. I discussed the 1-d case in the first blog and the 2-d case in the second. Here we discuss some of the properties of 2-d forecasting. Some readers may find some of my remarks surprising, even paradoxical.

**Written by:**Iain Currie

**Tags:**Filter information matrix by tag: forecasting, Filter information matrix by tag: splines, Filter information matrix by tag: P-splines, Filter information matrix by tag: penalty function, Filter information matrix by tag: mortality crossover

### Forecasting with penalty functions - Part II

Our first blog in this series of three looked at forecasting log mortality with penalties in one dimension, i.e. forecasting with data for a single age. We now look at the same problem, but in two dimensions. Figure 1 shows our data. We see an irregular surface sitting on top of the age-year plane. Just as in the 1-d case, we see an underlying smooth surface, and it is this surface that we wish both to estimate and to forecast.

**Written by:**Iain Currie

**Tags:**Filter information matrix by tag: forecasting, Filter information matrix by tag: splines, Filter information matrix by tag: P-splines, Filter information matrix by tag: penalty function, Filter information matrix by tag: mortality crossover

### Forecasting with penalty functions - Part I

There is much to say on the topic of penalty forecasting, so this is the first of three blogs. In this blog we will describe penalty forecasting in one dimension; this will establish the basic ideas. In the second blog we will discuss the case of most interest to actuaries: two-dimensional forecasting. In the final blog we will discuss some of the properties of penalty forecasting in two dimensions.

**Written by:**Iain Currie

**Tags:**Filter information matrix by tag: forecasting, Filter information matrix by tag: splines, Filter information matrix by tag: P-splines, Filter information matrix by tag: penalty function