Chapter 8. Regression with lagged explanatory variables

Most applications in finance are concerned with the analysis of time series data. However, most of the examples in Chapters 3 to 7 used cross-sectional data. This allowed us to build up the basic ideas underlying regression, including statistical concepts such as hypothesis testing and confidence intervals, in a simple manner. When working with time series variables, knowledge of such ideas is essential. However, some additional issues arise when working with time series data. The purpose of this chapter is to offer an introduction to these issues and to familiarize the reader with some concepts and notation used with time series models. After this introductory material, we take one step away in the direction of developing the models and methods that are used with financial time series.

The goal of the researcher working with time series data does not differ too much from that of the researcher working with cross-sectional data: both aim to develop a regression relating a dependent variable to some explanatory variables. However, the analyst using time series data will face two problems that the analyst using cross-sectional data will not encounter: (1) one time series variable can influence another with a time lag; and (2) if the variables are nonstationary, a problem known as spurious regression may arise.

At this stage, you are not expected to understand the second of these problems. The terms nonstationary, stationary and ...

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