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The autocorrelation of a periodic function is, itself, periodic with the same period. The autocorrelation of the sum of two completely uncorrelated functions (the cross-correlation is zero for all ) is the sum of the autocorrelations of each function separately.
The Breusch–Godfrey test is a test for autocorrelation in the errors in a regression model. It makes use of the residuals from the model being considered in a regression analysis, and a test statistic is derived from these. The null hypothesis is that there is no serial correlation of any order up to p. [3]
In this definition, it has been assumed that the stochastic variables are scalar-valued. If they are not, then more complicated correlation functions can be defined. For example, if X(s) is a random vector with n elements and Y(t) is a vector with q elements, then an n×q matrix of correlation functions is defined with , element
Cross-cultural research entails a particular statistical problem, known as Phylogenetic autocorrelation: tests of functional relationships (for example, a test of the hypothesis that societies with pronounced male dominance are more warlike) can be confounded because the samples of cultures are not independent. Traits can be associated not only ...
A plot showing 100 random numbers with a "hidden" sine function, and an autocorrelation (correlogram) of the series on the bottom. In the analysis of data, a correlogram is a chart of correlation statistics.
The run test is based on the null hypothesis that each element in the sequence is independently drawn from the same distribution. Under the null hypothesis, the number of runs in a sequence of N elements [ note 1 ] is a random variable whose conditional distribution given the observation of N + positive values [ note 2 ] and N − negative ...
Phylogenetic autocorrelation also known as Galton's problem, after Sir Francis Galton who described it, is the problem of drawing inferences from cross-cultural data, ...
The autocorrelation technique is a method for estimating the dominating frequency in a complex signal, as well as its variance. Specifically, it calculates the first two moments of the power spectrum, namely the mean and variance. It is also known as the pulse-pair algorithm in radar theory.