MultiCrossCorrelation Class |
Namespace: Imsl.Stat
The MultiCrossCorrelation type exposes the following members.
Name | Description | |
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MultiCrossCorrelation |
Constructor to compute the multichannel cross-correlation function of
two mutually stationary mulitchannel time series.
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Name | Description | |
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Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) | |
GetCrossCorrelation |
Returns the cross-correlations between the channels of x and
y.
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GetCrossCovariance |
Returns the cross-covariances between the channels of x and
y.
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GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
GetMeanX |
Returns an estimate of the mean of each channel of x.
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GetMeanY |
Returns an estimate of the mean of each channel of y.
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GetType | Gets the Type of the current instance. (Inherited from Object.) | |
GetVarianceX |
Returns the variances of the channels of x.
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GetVarianceY |
Returns the variances of the channels of y.
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MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
ToString | Returns a string that represents the current object. (Inherited from Object.) |
Name | Description | |
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NumberOfProcessors |
Perform the parallel calculations with the maximum possible number of
processors set to NumberOfProcessors.
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MultiCrossCorrelation estimates the multichannel cross-correlation function of two mutually stationary multichannel time series. Define the multichannel time series X by
where with n = x.GetLength(0) and p = x.GetLength(1). Similarly, define the multichannel time series Y by where with m = y.GetLength(0) and q = y.GetLength(1). The columns of X and Y correspond to individual channels of multichannel time series and may be examined from a univariate perspective. The rows of X and Y correspond to observations of p-variate and q-variate time series, respectively, and may be examined from a multivariate perspective. Note that an alternative characterization of a multivariate time series X considers the columns to be observations of the multivariate time series while the rows contain univariate time series. For example, see Priestley (1981, page 692) and Fuller (1976, page 14).Let = xmean be the row vector containing the means of the channels of X. In particular,
where for j = 1, 2, ..., p Let = ymean be similarly defined. The cross-covariance of lag k between channel i of X and channel j of Y is estimated by where i = 1, ..., p, j = 1, ..., q, and K = maximumLag. The summation on t extends over all possible cross-products with N equal to the number of cross-products in the sum.Let = xvar, where xvar is the variance of X, be the row vector consisting of estimated variances of the channels of X. In particular,
where Let = yvar, where yvar is the variance of Y, be similarly defined. The cross-correlation of lag k between channel i of X and channel j of Y is estimated by