pysteps.timeseries.autoregression.estimate_var_params_yw(gamma, d=0, check_stationarity=True)#

Estimate the parameters of a VAR(p) model

\(\mathbf{x}_{k+1}=\mathbf{\Phi}_1\mathbf{x}_k+ \mathbf{\Phi}_2\mathbf{x}_{k-1}+\dots+\mathbf{\Phi}_p\mathbf{x}_{k-p}+ \mathbf{\Phi}_{p+1}\mathbf{\epsilon}\)

from the Yule-Walker equations using the given correlation matrices \(\mathbf{\Gamma}_0,\mathbf{\Gamma}_1,\dots,\mathbf{\Gamma}_n\), where n=p.

  • gamma (list) – List of correlation matrices \(\mathbf{\Gamma}_0,\mathbf{\Gamma}_1,\dots,\mathbf{\Gamma}_n\). To obtain these matrices, use pysteps.timeseries.correlation.temporal_autocorrelation_multivariate() with window_radius=np.inf.

  • d ({0,1}) – The order of differencing. If d=1, the correlation coefficients gamma are assumed to be computed from the differenced time series, which is also done for the resulting parameter estimates.

  • check_stationarity (bool) – If True, the stationarity of the resulting VAR(p) process is tested. An exception is thrown if the process is not stationary.


out – List of VAR(p) coefficient matrices \(\mathbf{\Phi}_1, \mathbf{\Phi}_2,\dots\mathbf{\Phi}_{p+1}\), where the last matrix corresponds to the innovation term.

Return type



To estimate the parameters of an integrated VARI(p,d) model, compute the correlation coefficients gamma by calling pysteps.timeseries.correlation.temporal_autocorrelation_multivariate() with d>0. Estimation of the innovation parameter \(\mathbf{\Phi}_{p+1}\) is not currently implemented, and it is set to a zero matrix.