The Basics of Financial Econometrics: Tools, Concepts, and Asset Management Applications

CHAPTER 10

Cointegration

After reading this chapter you will understand:

• The concept of cointegration.
• The concept of spurious regressions.
• How to test for stationarity.
• How to test for cointegration using the Engle-Granger cointegration test.
• How to test for cointegration using the Johansen-Juselius cointegration test.
• How to identify multiple cointegration relations.

Financial time series data tend to exhibit trends. Trends can be deterministic or stochastic. In Chapter 5 we introduced the concept of a deterministic trend. To uncover a relationship among financial variables it is important to model changes in stochastic trends over time. Cointegration can be used to identify common stochastic trends among different financial variables. If financial variables are cointegrated, it can also be shown that the variables exhibit a long-run relationship. If this long-run relationship is severed, this may indicate the presence of a financial bubble.¹

The long-term relationships among financial variables, such as short-term versus long-term interest rates and stock prices versus dividends, have long interested finance practitioners. For certain types of trends, multiple regression analysis needs modification to uncover these relationships. A trend represents a long-term movement in the variable. One type of trend, a deterministic trend, has a straightforward solution. Since a deterministic trend is a function of time, we need merely include this time function in the regression. For example, ...