Search results
Results from the WOW.Com Content Network
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 ...
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
A two-terminal graph (TTG) is a graph with two distinguished vertices, s and t called source and sink, respectively. The parallel composition Pc = Pc(X,Y) of two TTGs X and Y is a TTG created from the disjoint union of graphs X and Y by merging the sources of X and Y to create the source of Pc and merging the sinks of X and Y to create the sink ...
In statistics, the autocorrelation of a real or complex random process is the Pearson correlation between values of the process at different times, as a function of the two times or of the time lag. Let { X t } {\displaystyle \left\{X_{t}\right\}} be a random process, and t {\displaystyle t} be any point in time ( t {\displaystyle t} may be an ...
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.
The correlation coefficient is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect inverse (decreasing) linear relationship (anti-correlation), [5] and some value in the open interval (,) in all other cases, indicating the degree of linear dependence between the variables. As it ...
Cointegration is a statistical property of a collection (X 1, X 2, ..., X k) of time series variables. First, all of the series must be integrated of order d.Next, if a linear combination of this collection is integrated of order less than d, then the collection is said to be co-integrated.
It is common practice in some disciplines (e.g. statistics and time series analysis) to normalize the autocovariance function to get a time-dependent Pearson correlation coefficient. However in other disciplines (e.g. engineering) the normalization is usually dropped and the terms "autocorrelation" and "autocovariance" are used interchangeably.