Aproximate Distributions of the Periodogram and Related Statistics under Normality

Seiji Nabeya and Katsuto Tanaka

Econometric Theory, 1986, vol. 2, issue 1, 33-65

Abstract: Under normality, we obtain higher-order approximations to the distributions of the periodogram and related statistics. Our approach is based on the theorem which decomposes the periodogram into the sum of two independent random variables. It is seen that this decomposition enables us to study fairly closely the higher-order properties of not only the periodogram, but also periodogram-based statistics such as the estimators of the spectrum and prediction error variance. Some of the approximation results are graphically presented together with the exact results based on simulations.

Date: 1986
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