4.7 Measurement of Spectral Correlation –Known Support Curves
In this section, for jointly SC processes the properly normalized frequency-smoothed cross-periodogram along a given support curve is considered as an estimator of the spectral cross-correlation density function on this support curve. Bias and covariance are determined. Moreover asymptotic unbiasedness, consistency, and asymptotic complex Normality are proved.
4.7.1 Mean-Square Consistency of the Frequency-Smoothed Cross-Periodogram
Assumption 4.7.1 Lack of Support-Curve Clusters (II). Let
be the set of indices of the curves 
, m ≠ n, that intercept 
in f.
There is no cluster of support curves. That is, for every 
and 
, the set 
is finite (or empty) and no curve 
with , can be arbitrarily close to the curve in f. That is, ...
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