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

ararray_like, 1d

coefficient for autoregressive lag polynomial, including zero lag

maarray_like, 1d

coefficient for moving-average lag polynomial, including zero lag


length of simulated time series


standard deviation of noise

distrvsfunction, random number generator

function that generates the random numbers, and takes sample size as argument default: np.random.randn TODO: change to size argument


Burn in observations at the generated and dropped from the beginning of the sample


sample of ARMA process given by ar, ma of length nsample


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.


>>> 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])