statsmodels.tsa.arima_process.ArmaProcess.impulse_response
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ArmaProcess.impulse_response(nobs=None)
[source] -
get the impulse response function (MA representation) for ARMA process
Parameters: ma : array_like, 1d
moving average lag polynomial
ar : array_like, 1d
auto regressive lag polynomial
nobs : int
number of observations to calculate
Returns: ir : array, 1d
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, nobs=100) ar_representation = arma_impulse_response(ma, ar, nobs=100)
fully tested against matlab
Examples
AR(1)
>>> arma_impulse_response([1.0, -0.8], [1.], nobs=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], nobs=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], nobs=10) array([ 1. , 1.3 , 1.24 , 0.992 , 0.7936 , 0.63488 , 0.507904 , 0.4063232 , 0.32505856, 0.26004685])
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