statsmodels.tsa.arima_process.ArmaProcess.impulse_response

ArmaProcess.impulse_response(leads=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
  • leads (int) – number of observations to calculate
Returns:

ir – impulse response function with nobs elements
Return type:

array, 1d

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])