A Bayesian Approach to Understanding Time Series Data

This paper explores the use of Bayesian models to analyze time series data. The Bayesian approach produces output that can be readily understood by actuaries and included in their own experience studies. We illustrate this Bayesian approach by analyzing U.S. unemployment rates, a macroeconomic time series. Understanding time series of macroeconomic variables can help actuaries in pricing and reserving their products. For example, a change in the level and/or variance of the unemployment series is of interest to actuaries, because its movement can explain a changing pattern of lapse rates of incidence rates. Our Bayesian analysis, based on models developed by McCulloch and Tsay (1993, 1994), allows for shifts in the level and in the error variance of a process. We develop a measure of model fit, based on the Akaike Information Criterion, that can be used in choosing between alternative models. Posterior prediction intervals for the fitted values are also created to pictorially show the range of paths that could result from the choice of a particular model.