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Roxana
Roxana
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Thanks for all the answers, after searching through literature I found out, indeed there is a systematic bias in estimating the autocorrelation of time-series with a finite-size. There is a series of old statistics papers discussing this bias and even they derived its analytical form for some cases like: Marriott, F. H. C., and J. A. Pope. "Bias in the estimation of autocorrelations." Biometrika 41.3/4 (1954): 390-402 (https://www.jstor.org/stable/2332719)

It seems, there are two major sources for the bias:

  • mean estimation of the finite-size time-series
  • correlation between covariance and variance (normalization part)

If we have a long enough time-series to better estimate the mean or use the true mean that we generated the data with, the negative bias that I observed in figures above will disappear.

Thanks for all the answers, after searching through literature I found out, indeed there is a systematic bias in estimating the autocorrelation of time-series with a finite-size. There is a series of old statistics papers discussing this bias and even they derived its analytical form for some cases like: https://www.jstor.org/stable/2332719

It seems, there are two major sources for the bias:

  • mean estimation of the finite-size time-series
  • correlation between covariance and variance (normalization part)

If we have a long enough time-series to better estimate the mean or use the true mean that we generated the data with, the negative bias that I observed in figures above will disappear.

Thanks for all the answers, after searching through literature I found out, indeed there is a systematic bias in estimating the autocorrelation of time-series with a finite-size. There is a series of old statistics papers discussing this bias and even they derived its analytical form for some cases like: Marriott, F. H. C., and J. A. Pope. "Bias in the estimation of autocorrelations." Biometrika 41.3/4 (1954): 390-402 (https://www.jstor.org/stable/2332719)

It seems, there are two major sources for the bias:

  • mean estimation of the finite-size time-series
  • correlation between covariance and variance (normalization part)

If we have a long enough time-series to better estimate the mean or use the true mean that we generated the data with, the negative bias that I observed in figures above will disappear.

Source Link
Roxana
Roxana
  • 41
  • 4

Thanks for all the answers, after searching through literature I found out, indeed there is a systematic bias in estimating the autocorrelation of time-series with a finite-size. There is a series of old statistics papers discussing this bias and even they derived its analytical form for some cases like: https://www.jstor.org/stable/2332719

It seems, there are two major sources for the bias:

  • mean estimation of the finite-size time-series
  • correlation between covariance and variance (normalization part)

If we have a long enough time-series to better estimate the mean or use the true mean that we generated the data with, the negative bias that I observed in figures above will disappear.