= Local periodogram smoothing
{title2=$\widehat f(\omega)=\sum_j w_{Tj}(\omega)I_T(\omega_j)$}
Average neighboring <periodogram> ordinates with nonnegative weights summing to one. Let the number $L_T$ of averaged ordinates tend to infinity while their frequency span, of order $L_T/T$, tends to zero. For a smooth <spectral density> and suitable short-memory or fourth-order dependence conditions, the bias tends to zero and variance is of order $1/L_T$. Smooth second-order spectral density alone does not ensure this: a time-constant random scale multiplying independent <white noise> has a smooth unconditional spectrum but a nonergodic random limiting local power.
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