A financial researcher is evaluating the relationship between a country's long-term interest rates and its inflation rate over the past 30 years. Initial analysis using standard OLS regression shows a statistically significant relationship. However, the Durbin-Watson statistic suggests the presence of positive autocorrelation, and a unit root test indicates that both series are I(1). The researcher suspects that the two series might be cointegrated. Which of the following statements about cointegration is most accurate in this context?
- ACointegration implies that the two series will always move in the same direction over time.
- BIf the series are cointegrated, their linear combination (residuals from the regression) will be stationary.
- CTesting for cointegration is only necessary if both series are I(0).
- DCointegration suggests that standard OLS regression is appropriate for modeling their short-run relationship.
Show answer & explanationAnswer & explanation
Correct answer: B. If the series are cointegrated, their linear combination (residuals from the regression) will be stationary.
Cointegration means that while individual non-stationary time series (like I(1) series) may wander, a linear combination of them is stationary. In a regression context, this means the residuals from the regression of one I(1) series on another I(1) series will be stationary, indicating a long-run equilibrium relationship.
Why the other options are wrong
- A. Cointegration implies a long-run equilibrium relationship, but it doesn't mean the series always move in the same direction in the short run. They can diverge temporarily but revert to their long-run relationship.
- C. Testing for cointegration is specifically necessary when two or more time series are non-stationary (e.g., I(1)) but are believed to have a long-run equilibrium relationship. If series are I(0), they are already stationary, and cointegration testing is not required.
- D. If series are I(1) and not cointegrated, standard OLS regression can lead to spurious regression results. If they are cointegrated, OLS can provide consistent estimates of the long-run relationship, but for short-run dynamics and correcting for disequilibrium, an Error Correction Model (ECM) is often more appropriate.
Cointegration
Cointegration describes a long-run equilibrium relationship between two or more non-stationary time series (typically I(1)) such that a linear combination of them is stationary (I(0)), implying that they move together in the long run despite short-term deviations.
- Applies to non-stationary series (e.g., I(1)).
- Residuals from their regression must be stationary (I(0)).
- Indicates a stable long-run relationship.
- Leads to the use of Error Correction Models (ECM) for short-run dynamics.
Memory trick: Cointegration: Non-stationary series, stationary residuals, long-run link.