statsmodels.tsa.arima_process.ArmaProcess.impulse_response¶

ArmaProcess.impulse_response(leads=None)[source]¶

Compute the impulse response function (MA representation) for ARMA process.

Parameters:

leadsint: 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])