Book contents
- Frontmatter
- Contents
- Preface
- 1 Regression and the Normal Distribution
- Part I Linear Regression
- Part II Topics in Time Series
- 7 Modeling Trends
- 8 Autocorrelations and Autoregressive Models
- 9 Forecasting and Time Series Models
- 10 Longitudinal and Panel Data Models
- Part III Topics in Nonlinear Regression
- Part IV Actuarial Applications
- Brief Answers to Selected Exercises
- Appendix 1 Basic Statistical Inference
- Appendix 2 Matrix Algebra
- Appendix 3 Probability Tables
- Index
8 - Autocorrelations and Autoregressive Models
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Regression and the Normal Distribution
- Part I Linear Regression
- Part II Topics in Time Series
- 7 Modeling Trends
- 8 Autocorrelations and Autoregressive Models
- 9 Forecasting and Time Series Models
- 10 Longitudinal and Panel Data Models
- Part III Topics in Nonlinear Regression
- Part IV Actuarial Applications
- Brief Answers to Selected Exercises
- Appendix 1 Basic Statistical Inference
- Appendix 2 Matrix Algebra
- Appendix 3 Probability Tables
- Index
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.
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- Information
- Regression Modeling with Actuarial and Financial Applications , pp. 251 - 272Publisher: Cambridge University PressPrint publication year: 2009