= Periodogram
{title2=$I_T(\lambda)$}
For a centered record of length $T$, the periodogram is the squared modulus of its <discrete Fourier transform>, with normalization
$$
I_T(\lambda)=\frac1{2\pi T}\left|\sum_{t=1}^TX_te^{-it\lambda}\right|^2.
$$
Under suitable short-memory assumptions its expectation approaches the <spectral density of a stationary process>, but its variance generally does not vanish. Smoothing nearby frequencies can provide an estimate with <statistical consistency>.
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