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We present an approximate expression for the covariance of the log-averageperiodogram for a zero mean stationary Gaussian process. Our findings extendthe work of Ephraim and Roberts (2005) on the covariance of the log-periodogramby additionally taking averaging over local frequencies into account. Moreover,we provide a simple expression for the non-integer moments of a non-centralchi-squared distribution.

On second-order statistics of the log-average periodogram