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  "body": "\n## Summary\n\nThe Whittle likelihood approximates the Gaussian likelihood of a stationary time series using the [[periodogram|3ZYM0HXA3E]] and the model spectral density.\nIt replaces a large covariance matrix by a sum over frequencies, which makes estimation fast.\nPeter Whittle introduced it in the 1950s, and maximizing it gives estimators with the same first-order asymptotic behaviour as Gaussian maximum likelihood.\n\n## Explanations\n\n### L1 human\n\nNeighbouring values of a time series are dependent, which makes the exact likelihood awkward to compute.\nAfter a Fourier transform, the values at different frequencies are nearly independent.\nThe Whittle likelihood treats them as independent, each with a spread given by the model's spectrum at that frequency.\nFitting a model then means matching the model spectrum to the observed periodogram, frequency by frequency.\n",
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