Cointegration

#Statistics

Cointegration is statistical concept in econometrics that describes a long-term relationship between two or more non-stationary time series variables. It indicates that although the individual variables may be non-stationary, there exists a linear combination of them that is stationary, allowing for meaningful analysis of their relationship over time.

Alternative Definition

Cointegration is a statistical concept that describes a long-term equilibrium relationship between two or more non-stationary time series. This phenomenon occurs when the time series, while individually non-stationary, can be combined in such a way that their linear combination results in a stationary series. This implies that the series share a common stochastic trend, allowing them to move together over time around a stable mean.

Key Characteristics of Cointegration

  1. Nonstationarity: Each time series involved must be non-stationary, typically meaning they have unit roots (integrated or order one, denoted as l(1)).
  2. Stationary Linear Combination: There exists at least one linear combination of the non-stationary series that is stationary (integrated of order less than one).
  3. Lon-Run Equilibrium: Cointegrated series maintain a long-run equilibrium relationship, suggesting that deviations from this equilibrium are temporary and will revert over time.