Unformatted text preview: ure that, as the sample size grows, the window width goes to zero, but includes an infinite number of terms. The conditions on the spectral window function Wn ensure that ^ the expectation of f () converges to f () and its variance converges to zero. 8 Consistency of nonparametric spectral estimation
^ E f () =
|j|Ln Wn (j)E I(^(n) - j/n) Wn (j)f () = f (). ^ Var f () = |j|Ln j,k Wn (j)Wn (k)Cov I(^(n) - j/n), I(^(n) - k/n) 2 Wn (j)Var I(^(n) - j/n) 2 Wn (j) 0. j f 2 () j 9 Introduction to Time Series Analysis. Lecture 21.
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- Fall '08
- Signal Processing, Wn, Estimation theory, Weighted mean, Weight function, Time series analysis