Explain the concept of cointegration in time series analysis.

Instruction: Discuss what cointegration means and how it can be used in analyzing paired time series data.

Context: This question tests the candidate's understanding of cointegration, a concept critical for analyzing relationships between two or more time series in the long term.

Updated

Example Answer

In the common I(1) case, individual series have unit roots but a particular linear combination is stationary. That combination represents a long-run relationship, even though the individual levels wander. Two series trending upward together are not enough to establish cointegration.

I would check the integration assumptions and choose a test suited to the system. An Engle-Granger test estimates a candidate relationship and tests its residuals using cointegration-specific critical values, rather than an ordinary ADF p-value as if the relationship were known in advance. For a cointegrated system, an error-correction model can represent short-run changes and adjustment toward the long-run relation. I would also examine structural breaks; historical cointegration is not a guarantee of profitable trading or future stability.

Make it your own

Use a plausible pair or system and explain why a stable long-run relationship might exist.

Why this works

It includes the assumptions and avoids turning a statistical relation into a trading promise.

Follow-up to practice

Why are ordinary residual ADF critical values insufficient?

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