J f 2 j 9 introduction to time series analysis lecture

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Unformatted text preview: view: The periodogram, the smoothed periodogram. 2. Other smoothed spectral estimators. 3. Consistency. 4. Asymptotic distribution. 10 Nonparametric spectral estimation: asymptotics Recall that for Daniell's estimator we have ^(k ) = 1 f L (L-1)/2 2 2 Xc (k - l/n) + Xs (k - l/n) , l=-(L-1)/2 which is (asymptotically) a sum of 2L independent 2 random variables, so 1 2 ^ f (k ) f (k ) 2L . 2L But for a non-uniform weighting, we form a weighted sum of these 2 1 random variables, so we cannot count up the degrees of freedom in the same way. But we can still approximate a general smoothed spectrum by ^ f (k ) ck 2 for som...
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