Chapter Preview. This chapter deals with the analysis of measurements over time, called time series analysis. Examples of time series include inflation and unemployment indices, stock prices, currency cross rates, monthly sales, the quarterly number of claims made to an insurance company, outstanding liabilities of a company over time, internet traffic, temperature and rainfall, and the number of mortgage defaults. Time series analysis aims to explain and model the relationship between values of the time series at different points of time. Models include ARIMA, structural, and stochastic volatility models and their extensions. The first two classes of models explain the level and expected future level of a time series. The last class seeks to model the change over time in variability or volatility of a time series. Time series analysis is critical to prediction and forecasting. This chapter explains and summarizes modern time series modeling as used in insurance, actuarial studies, and related areas such as finance. Modeling is illustrated with examples, analyzed with the R statistical package.

Exploring Time Series Data

17.1.1 Time Series Data

A time series is a sequence of measurements y1, y2, …, yn made at consecutive, usually regular, points in time. Four time series are plotted in Figure 17.1 and explained in detail later. Each time series is “continuous,” meaning each yt can attain any value in some interval of the line.