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I have an oscillating time series which has a Lorentzian shaped power spectrum, centered about a dominant frequency.

After taking the autocorrelation of this time series, I see that it's nearly always positive.

Here's the normalized autocorrelation of my time series:

enter image description here

(a) is a zoomed out autocorrelation, and (b) is zooming into that short time region.

It's an oscillating time series, so the autocorrelation is oscillating as expected.

How can the autocorrelation almost always be positive though?

I'm confused because the autocorrelation of a sinusoid is another sinusoid, which oscillates between both positive and negative. My autocorrelation, however, oscillates only in the positive regime... What would cause this?

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    $\begingroup$ It's unclear how you're concluding that the autocorrelation of your signal is almost always positive. All your graphs show is a time-series of "normalized amplitude", and it is not clear what that is in this context. $\endgroup$
    – Ben
    Commented Jan 9, 2022 at 23:36
  • $\begingroup$ @Ben Sorry, edited for clarification. That normalized amplitude IS my autocorrelation - it's the normalized amplitude of my autocorrelation. $\endgroup$
    – Thermodynamix
    Commented Jan 9, 2022 at 23:46
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    $\begingroup$ HI: Are you de-meaning the series before you calculate the auto-correlation. if not, you should and that may give you more of the result you expect to see. you don't want to have a non-zero mean series because the acf should be calculated on a series that has a mean of zero. Note that what I'm saying here pertains to the statistical calculation of auto-correlation. dsp people have a different way of defining the auto-correlation so, if you're working in dsp, you should probably ask on dsp.stackexchange. They have a pretty different way of defining it. $\endgroup$
    – mlofton
    Commented Jan 10, 2022 at 5:57

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If you make your harmonic signal to have a zero mean you'd see the auto correlation have more negative values.

Since your signal is almost always positive and the correlation is a sum of the values it makes sense it will be almost always positive.

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  • $\begingroup$ Yeah that's exactly it. If the signal oscillates about zero, then the autocorrelation will behave the same (at least for nearly harmonic signals). $\endgroup$
    – Thermodynamix
    Commented Jan 11, 2022 at 16:26

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