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

  • 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

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

Return type:



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])