Cointegrator

A cointegrator is a mathematical or statistical concept used in time series analysis. It refers to a linear combination of two or more non-stationary time series that is stationary. In simpler terms, if two or more time series tend to move together in the long run, even though they might drift apart in the short term, they are considered cointegrated.

The concept is particularly important in econometrics and finance. Non-stationary time series, such as stock prices or GDP, can often lead to spurious regressions, where a statistically significant relationship is found between variables that are not truly related. Cointegration provides a way to identify genuine long-term relationships between such series.

If a set of time series is cointegrated, it implies that there is an underlying equilibrium relationship between them. Deviations from this equilibrium are temporary and are expected to be corrected over time. This property makes cointegration useful for developing trading strategies, such as pairs trading, where one might buy the relatively undervalued asset and sell the relatively overvalued asset in a cointegrated pair.

The process of testing for cointegration typically involves examining the residuals of a regression between the non-stationary series. If these residuals are stationary, then the original series are cointegrated. Various statistical tests, like the Engle-Granger test or the Johansen test, are used for this purpose. The number of cointegrating relationships in a set of series is determined by the rank of a specific matrix.