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
7 - Modeling Trends
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 begins our study of time series data by introducing techniques to account for major patterns, or trends, in data that evolve over time. The focus is on how regression techniques developed in earlier chapters can be used to model trends. Further, new techniques, such differencing data, allow us to naturally introduce a random walk, an important model of efficient financial markets.
Introduction
Time Series and Stochastic Processes
Business firms are not defined by physical structures such as the solid stone bank building that symbolizes financial security. Nor are businesses defined by spacealien invader toys that they manufacture for children. Businesses comprise several complex, interrelated processes. A process is a series of actions or operations that lead to a particular end.
Processes not only are the building blocks of businesses but also provide the foundations for our everyday lives. We may go to work or school every day, practice martial arts, or study statistics. These are regular sequences of activities that define us. In this text, our interest is in modeling stochastic processes, defined as ordered collections of random variables that quantify a process of interest.
Some processes evolve over time, such as daily trips to work or school, or the quarterly earnings of a firm. We use the term longitudinal data for measurements of a process that evolves over time.
- Type
- Chapter
- Information
- Regression Modeling with Actuarial and Financial Applications , pp. 227 - 250Publisher: Cambridge University PressPrint publication year: 2009