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.
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, ...