# pysteps.timeseries.autoregression.estimate_ar_params_yw_localized#

pysteps.timeseries.autoregression.estimate_ar_params_yw_localized(gamma, d=0)#

Estimate the parameters of a localized AR(p) model

$$x_{k+1,i}=\phi_{1,i}x_{k,i}+\phi_{2,i}x_{k-1,i}+\dots+\phi_{p,i}x_{k-p,i}+\phi_{p+1}\epsilon$$

from the Yule-Walker equations using the given set of autocorrelation coefficients :mathgamma_{l,i}, where :mathl denotes time lag and $$i$$ denote spatial coordinates with arbitrary dimension.

Parameters
• gamma (array_like) – A list containing the lag-l temporal autocorrelation coefficient fields 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.

Returns

out – List of length p+1 containing the AR(p) parameter fields for for the lag-p terms and the innovation term. The parameter fields have the same shape as the elements of gamma.

Return type

list

Notes

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 and window_radius<np.inf.