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

Estimate the parameters of an AR(p) model

\(x_{k+1}=\phi_1 x_k+\phi_2 x_{k-1}+\dots+\phi_p x_{k-p}+\phi_{p+1}\epsilon\)

from the Yule-Walker equations using the given set of autocorrelation coefficients.

  • gamma (array_like) – Array of length p containing the lag-l temporal autocorrelation coefficients for l=1,2,…p. The correlation coefficients are assumed to be in ascending order with respect to time lag.

  • 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 – Array of length p+1 containing the AR(p) parameters for for the lag-p terms and the innovation term.

Return type



To estimate the parameters of an integrated ARI(p,d) model, compute the correlation coefficients gamma by calling pysteps.timeseries.correlation.temporal_autocorrelation() with d>0.