Cointegration – time series with a shared trend

We briefly mentioned cointegration in the previous section on multivariate time-series models. Let's now explain this concept and how to diagnose its presence in more detail before leveraging it for a statistical arbitrage trading strategy.

We have seen how a time series can have a unit root that creates a stochastic trend and makes the time series highly persistent. When we use such an integrated time series in their original, rather than in differenced, form as a feature in a linear regression model, its relationship with the outcome will often appear statistically significant, even though it is not. This phenomenon is called spurious regression (for details, see Chapter 18, CNNs for Financial Time Series and Satellite Images, in Wooldridge, 2008). Therefore, the recommended solution is to difference the time series so they become stationary before using them in a model.

However, there is an exception when there...