mesmer.stats.localized_covariance.adjust_covariance_ar1(covariance, ar_coefs)#

adjust localized empirical covariance matrix for autoregressive process of order one

  • covariance (2D xr.DataArray) – Empirical covariance matrix.

  • ar_coefs (1D xr.DataArray) – The coefficients of the autoregressive process of order 1. Must have length equal to the size of covariance.


adjusted_covariance (xr.DataArray) – Adjusted empirical covariance matrix.


  • Adjusts covariance for an AR(1) process according to [1], eq (8).

  • The formula is specific for an AR(1) process, see also #167 (comment).

  • According to [2] “The multiplication with the reduction_factor scales the empirical standard error under the assumption of an autoregressive process of order one [3]. This accounts for the fact that the variance of an autoregressive process is larger than that of the driving white noise process.”

  • This formula is wrong in [1]. However, it is correct in the code. See also [2] and [3].