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In time series analysis and statistics, the cross-correlation of a pair of random process is the correlation between values of the processes at different times, as a function of the two times. Let ( X t , Y t ) {\displaystyle (X_{t},Y_{t})} be a pair of random processes, and t {\displaystyle t} be any point in time ( t {\displaystyle t} may be ...
In particular, it is possible to have serial dependence but no (linear) correlation. In some fields however, the two terms are used as synonyms. A time series of a random variable has serial dependence if the value at some time in the series is statistically dependent on the value at another time . A series is serially independent if there is ...
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
Cross-covariance may also refer to a "deterministic" cross-covariance between two signals. This consists of summing over all time indices. For example, for discrete-time signals f [ k ] {\displaystyle f[k]} and g [ k ] {\displaystyle g[k]} the cross-covariance is defined as
In the analysis of data, a correlogram is a chart of correlation statistics. For example, in time series analysis, a plot of the sample autocorrelations versus (the time lags) is an autocorrelogram. If cross-correlation is plotted, the result is called a cross-correlogram.
A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. [1] If one considers the correlation function between random variables representing the same quantity measured at two different points, then this is often referred to as an ...
Scaled correlation between two signals is defined as the average correlation computed across short segments of those signals. First, it is necessary to determine the number of segments K {\displaystyle K} that can fit into the total length T {\displaystyle T} of the signals for a given scale s {\displaystyle s} :
Transfer entropy is a non-parametric statistic measuring the amount of directed (time-asymmetric) transfer of information between two random processes. [1] [2] [3] Transfer entropy from a process X to another process Y is the amount of uncertainty reduced in future values of Y by knowing the past values of X given past values of Y.