5.5 Proofs for Section 4.7.1 “Mean-Square Consistency of the Frequency-Smoothed Cross-Periodogram”
In this section, proofs of lemmas and theorems presented in Section 4.7.1 on the mean-square consistency of the frequency-smoothed cross-periodogram are reported.
Lemma 5.5.1 Let W(f) be a.e. continuous and regular as |f|→ ∞, and (that is, W can be either WA satisfying Assumption 4.4.5 or WB satisfying Assumption 4.6.2). We have the following results.