Difference in the estimation of the AR noise variance

[lionelkusch]

The formula from wikipedia for the estimation of the variance of an AR process is:
$VAR(X_t)=\frac{\sigma_\epsilon^2}{1-\phi^2}$ where $\sigma_\epsilon$ is the standard deviation of the noise and $\phi\ is the coefficient of autoregression.
There is a small difference with the actual implementation:

hidimstat/src/hidimstat/noise_std.py

Line 246 in fbfd68f

sigma_hat[:] = sigma_eps / np.sqrt((1 - np.dot(coef_ar, rho_ar[1:])))

$VAR(X_t)=\frac{\sigma_\epsilon}{1-B.\Phi}$ where $\sigma_\epsilon$ is the standard deviation of the noise, $B_n$ are the autocovariance coefficients and $\Phi$ the autocorrelation coefficients .

          This would deserve a small study. I'd rather remove the comment here and open an issue.

Originally posted by @bthirion in #127 (comment)