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The definition of the autocorrelation coefficient of a stochastic ... The traditional test for the presence of first-order autocorrelation is the Durbin ...
Plotting the partial autocorrelation function and drawing the lines of the confidence interval is a common way to analyze the order of an AR model. To evaluate the order, one examines the plot to find the lag after which the partial autocorrelations are all within the confidence interval. This lag is determined to likely be the AR model's order ...
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 i , j ...
Correlogram example from 400-point sample of a first-order autoregressive process with 0.75 correlation of adjacent points, along with the 95% confidence intervals (plotted about the correlation estimates in black and about zero in red), as calculated by the equations in this section.
The autocorrelation function of an AR(p) process is a sum of decaying exponentials. Each real root contributes a component to the autocorrelation function that decays exponentially. Similarly, each pair of complex conjugate roots contributes an exponentially damped oscillation.
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [ a ] The variables may be two columns of a given data set of observations, often called a sample , or two components of a multivariate random variable with a known distribution .
Priestley uses stationary up to order m if conditions similar to those given here for wide sense stationarity apply relating to moments up to order m. [ 3 ] [ 4 ] Thus wide sense stationarity would be equivalent to "stationary to order 2", which is different from the definition of second-order stationarity given here.
It can be computationally expensive to solve the linear regression problems. Actually, the nth-order partial correlation (i.e., with |Z| = n) can be easily computed from three (n - 1)th-order partial correlations. The zeroth-order partial correlation ρ XY·Ø is defined to be the regular correlation coefficient ρ XY.