statsmodels.tsa.arima_process.arma_impulse_response¶
-
statsmodels.tsa.arima_process.
arma_impulse_response
(ar, ma, leads=100)[source]¶ Compute the impulse response function (MA representation) for ARMA process.
- Parameters
- ararray_like, 1d
The auto regressive lag polynomial.
- maarray_like, 1d
The moving average lag polynomial.
- leads
int
The number of observations to calculate.
- Returns
ndarray
The impulse response function with nobs elements.
Notes
This is the same as finding the MA representation of an ARMA(p,q). By reversing the role of ar and ma in the function arguments, the returned result is the AR representation of an ARMA(p,q), i.e
ma_representation = arma_impulse_response(ar, ma, leads=100) ar_representation = arma_impulse_response(ma, ar, leads=100)
Fully tested against matlab
Examples
AR(1)
>>> arma_impulse_response([1.0, -0.8], [1.], leads=10) array([ 1. , 0.8 , 0.64 , 0.512 , 0.4096 , 0.32768 , 0.262144 , 0.2097152 , 0.16777216, 0.13421773])
this is the same as
>>> 0.8**np.arange(10) array([ 1. , 0.8 , 0.64 , 0.512 , 0.4096 , 0.32768 , 0.262144 , 0.2097152 , 0.16777216, 0.13421773])
MA(2)
>>> arma_impulse_response([1.0], [1., 0.5, 0.2], leads=10) array([ 1. , 0.5, 0.2, 0. , 0. , 0. , 0. , 0. , 0. , 0. ])
ARMA(1,2)
>>> arma_impulse_response([1.0, -0.8], [1., 0.5, 0.2], leads=10) array([ 1. , 1.3 , 1.24 , 0.992 , 0.7936 , 0.63488 , 0.507904 , 0.4063232 , 0.32505856, 0.26004685])