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  "body": "\n## Summary\n\nSpectral density estimation is the problem of estimating the spectral density of a stationary process from a finite stretch of data.\nThe spectral density describes how the variance of the process is spread over frequencies.\nThe raw [[periodogram|3ZYM0HXA3E]] is too noisy for this, so practical estimators smooth it over nearby frequencies or fit a parametric model.\nSpectral estimates reveal periodic components and the memory structure of a series and are used in signal processing, economics and geophysics.\n\n## Explanations\n\n### L1 human\n\nA stationary signal can be thought of as a mix of waves of many frequencies with random amplitudes.\nIts spectral density says how much power each frequency carries, like the bars of a music equalizer.\nFrom a recording of finite length, these bars can only be estimated, and a naive estimate flickers wildly from one frequency to the next.\nAveraging over neighbouring frequencies, or over several pieces of the recording, gives a steadier picture at the cost of some blurring.\n",
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