This candidate forecasts average claim severity in personal auto insurance.

Your regression analysis and time series student projects can use data from actuarial work: pure premium relativities for class ratemaking, claim frequency, claim severity, policyholder retention rates, mortality, morbidity, and disability rates, dozens of other data sets.

One might think that actuaries use sophisticated statistical models to project claim frequency and severity, since these items are essential for determining pure premiums. Some insurers do excellent work, examining the characteristics of their books of business to form optimal models for claim frequency and severity. Other insurers use traditional techniques that can easily be improved.

For a student project that will be useful to your company, examine claim frequency or severity, policyholder retention rates, and similar ratemaking data. Some insurers fit claim severity to an exponential curve and apply the fitted trend rate to each year’s claim severity. This is the simple (non-stochastic) autoregressive trend model discussed in the early modules of the time series course.

Your student project may examine ARIMA and structural models that improve the forecasts. Use your company’s current method as the base case, and compare in-sample and out-of-sample goodness-of-fit tests with your ARIMA and structural models.

For your ARIMA model, form a stationary process from your claim severity or frequency data. For claim severity, take logarithms and first differences. For the student project, examine the graph of the data and the correlogram, and explain why logarithms and first differences are needed.

If you have quarterly data, you can use quarterly claim frequency and severity figures. Claim frequency and severity are often seasonal. You can de-seasonalize the data or you can use an AR(4) term. Examine the effects of the alternative methods and select the one that seems best.

Examine several models, such as ARIMA(1,1,0), ARIMA(2,1,0), ARIMA(0,1,1), and ARIMA(1,1,1). Use the in-sample goodness-of-fit tests to pick the optimal ARIMA process. If two models seem equally good, use out-of-sample tests to choose between them. Often a more complex model has a better in-sample fit, but a simpler model has better out-of-sample forecasts.

Set up an out-of-sample test between your ARIMA model and your company’s current ratemaking method. Make predictions for the next four quarters from each model, show them to your manager, and see which model forecasts better over the next year. It is likely – but not certain – that your model will do better.

In many cases (including claim frequency and severity projections), the ARIMA processes are better applied to the residuals. For a structural model, determine the optimal inflation index to use for claim severity and the optimal macroeconomic variables to use for claim frequency. You can find papers by Masterson published in the Proceedings of the CAS, and some recent papers using ARIMA processes published in the CAS Forum, that address these topics.

Develop a structural model, using inflation forecasts published by consulting firms. If you don’t have access to these forecasts, use your own forecasts of inflation by ARIMA modeling on the inflation indices. Regress your claim severity time series on the inflation index and apply an ARIMA process to the residuals.

Set up an out-of-sample test for the next four quarters. If your model does better than the company’s current procedures, you will get immediate credit (and perhaps a raise). If your model does not do better, you lose nothing. You will have received VEE credit and you learned much about claim frequency and severity.

Don’t wait four quarters to write up your student project. Send in your student project when you complete the modeling. A year later, you can write back to NEAS reporting the results of the comparison between your model and the company’s current procedures.