Coherence (statistics) 

For a different sense of the word "coherence" that is also sometimes used in statistics, see coherence (philosophical gambling strategy).

In probability theory and statistics, coherence, like correlation, gives a measure of the dependence of two random variables. Often these two random variables are time series, and therefore, coherence is seen as a time series analogue of the correlation coefficient. The coherence of random variables X and Y is defined as

\gamma^2 = { \left|\mathrm{E} ( X^{^*} Y ) \right|^2 \over \mathrm{E}(\left|X\right|^2) \mathrm{E}(\left|Y\right|^2)}\,

where |X| indicates absolute magnitude, X* is the complex conjugate of X, and E(X) denotes the expected value of a random variable X.

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