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cointegration
Cointegration is a statistical property of a collection (X1,X2,...,Xk) of time series variables. First, all of the series must be integrated of order 1 (see Order of Integration). Next, if a linear combination of this collection is integrated of order zero, then the collection is said to be co-integrated. Formally, if (X,Y,Z) are each integrated of order 1, and there exist coefficients a,b,c such that aX+bY+cZ is integrated of order 0, then X,Y, and Z are cointegrated. Cointegration has become an important property in contemporary time series analysis. Time series often have trends—-either deterministic or stochastic. In a seminal paper, Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends—these are also called unit root processes, or processes integrated of order 1—I(1). They also showed that unit root processes have non-standard statistical properties, so that conventional econometric theory methods do not apply to them.
==Introduction==
If two or more series are individually integrated (in the time series sense) but some linear combination of them has a lower order of integration, then the series are said to be cointegrated. A common example is where the individual series are first-order integrated (I(1)) but some (cointegrating) vector of coefficients exists to form a stationary linear combination of them. For instance, a stock market index and the price of its associated futures contract move through time, each roughly following a random walk. Testing the hypothesis that there is a statistically significant connection between the futures price and the spot price could now be done by testing for the existence of a cointegrated combination of the two series.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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