statsmodels.tsa.arima_process.arma_generate_sample

statsmodels.tsa.arima_process.arma_generate_sample(ar, ma, nsample, sigma=1, distrvs=<built-in method randn of mtrand.RandomState object>, burnin=0) [source]

Generate a random sample of an ARMA process

Parameters:	ar (array_like, 1d) – coefficient for autoregressive lag polynomial, including zero lag ma (array_like, 1d) – coefficient for moving-average lag polynomial, including zero lag nsample (int) – length of simulated time series sigma (float) – standard deviation of noise distrvs (function, random number generator) – function that generates the random numbers, and takes sample size as argument default: np.random.randn TODO: change to size argument burnin (integer) – Burn in observations at the generated and dropped from the beginning of the sample
Returns:	sample – sample of ARMA process given by ar, ma of length nsample
Return type:	array

Notes

As mentioned above, both the AR and MA components should include the coefficient on the zero-lag. This is typically 1. Further, due to the conventions used in signal processing used in signal.lfilter vs. conventions in statistics for ARMA processes, the AR parameters should have the opposite sign of what you might expect. See the examples below.

Examples

>>> import numpy as np
>>> np.random.seed(12345)
>>> arparams = np.array([.75, -.25])
>>> maparams = np.array([.65, .35])
>>> ar = np.r_[1, -arparams] # add zero-lag and negate
>>> ma = np.r_[1, maparams] # add zero-lag
>>> y = sm.tsa.arma_generate_sample(ar, ma, 250)
>>> model = sm.tsa.ARMA(y, (2, 2)).fit(trend='nc', disp=0)
>>> model.params
array([ 0.79044189, -0.23140636,  0.70072904,  0.40608028])