8 - Autocorrelations and Autoregressive Models

Summary

Chapter Preview. This chapter continues our study of time series data. Chapter 7 introduced techniques for determining major patterns that provide a good first step for forecasting. Chapter 8 provides techniques for detecting subtle trends in time and models to accommodate these trends. These techniques detect and model relationships between the current and past values of a series using regression concepts.

Autocorrelations

Application: Inflation Bond Returns

To motivate the introduction of methods in this chapter, we work in the context of the inflation bond return series. Beginning in January 2003, the U.S. Treasury Department established an inflation bond index that summarizes the returns on long-term bonds offered by the Treasury Department that are inflation indexed. For a Treasury inflation-protected security (TIPS), the principal of the bond is indexed by the (three-month-lagged) value of the (non-seasonally-adjusted) consumer price index. The bond then pays a semiannual coupon at a rate determined at auction when the bond is issued. The index that we examine is the unweighted average of bid yields for all TIPS with remaining terms to maturity of 10 or more years.

Monthly values of the index from January 2003 through March 2007 are considered, for a total of T = 51 returns. Atime series plot of the data is presented in Figure 8.1. This plot suggests that the series is stationary, and so it is useful to examine the distribution of the series through summary statistics that appear in Table 8.1.