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The log of the periodogram is used to estimate the innovation variance of a stationary time series. The difference between the log of the estimated variance of the process and the log of the estimated innovation variance is used as a test for white noise. It is shown that this test is equivalent to Bartlett's test for homogeneity of variances applied to the periodogram without grouping and the asymptotic properties are derived.
Davis et al. (Fri,) studied this question.