Sample Question #85 (econometrics – time series)

What is cointegration? How do you test for cointegration? What’s an example of a cointegration application?

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Sample Question #85 (econometrics – time series)

What is cointegration? How do you test for cointegration? What’s an example of a cointegration application?

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ANSWER

Cointegration refers to the econometric relationship between two or more time series that, while nonstationary with a unit root themselves, have a linear combination of the two that is stationary. More formally, let y be a vector time series (i.e., each component of y is a time series). While each y(i) is nonstationary with unit root, there exists some nonzero scalar vector a so that a’y is stationary.

Testing for cointegration is complicated. First, you should recall that the null hypothesis is there is no cointegration, i.e., all linear combinations of the components of y have unit root. Second, you should know there are two cases to consider, one is if the vector a has a known candidate value (e.g., as suggested by economic theory), and the other is if the vector a is totally unknown. Third, you need to know one testing procedure, the Engle-Granger two-step test.

In finance, there are many applications of cointegration. Many statistical arbitrage models, for instance, rely on the cointegration between two stocks’ prices. Another example is the S&P 500 index and its futures price.