Calculates the
series1 |
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A series or array. |
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series2 |
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A series or array. |
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norm |
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Optional. An integer, the normalization method:
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W3 displays the cross-covariance of a sine wave normalized to -1 and 1. W4 shows the cross-covariance between a sine wave and random noise. The normalized maximum of W3 is 1.0, indicating perfect covariance at time t = 0. Although the series of W4 displays some peaks, the normalized maximum is roughly 0.04, indicating little covariance between W1 and W2. For a graphical representation, OVERPLOT W4 in W3.
where E is the expected value operator, x[n] and y[n] are a stationary random processes, μx and μy are the mean values and * indicates complex conjugate. In practice, the
The zeroth lag component is the mid point of the series.
The BIASED normalization divides the result by N, the maximum length of the input series.
The UNBIASED normalization divides the result by
where i is the index of the result with a start value of 1. For a 0 start index, the unbiased estimate becomes: