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Chapter

10

Cointegration

a

fter 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, if the variables are increasing or decreasing as
a linear function of time, we may simply include time as a variable in the
(^1) A financial bubble is defined as a situation where asset price increases are sharper
than justified by the fundamental investment attributes of the asset.