pysteps.timeseries.autoregression.estimate_ar_params_yw_localized
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 :math`gamma_{l,i}`, where :math`l` 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.