statsmodels.tsa.arima_process.arma_generate_sample(ar, ma, nsample, scale=1, distrvs=None, axis=0, burnin=0)[source]

Simulate data from an ARMA.


The coefficient for autoregressive lag polynomial, including zero lag.


The coefficient for moving-average lag polynomial, including zero lag.

nsampleint or tuple of ints

If nsample is an integer, then this creates a 1d timeseries of length size. If nsample is a tuple, creates a len(nsample) dimensional time series where time is indexed along the input variable axis. All series are unless distrvs generates dependent data.


The standard deviation of noise.

distrvsfunction, random number generator

A function that generates the random numbers, and takes size as argument. The default is np.random.standard_normal.


See nsample for details.


Number of observation at the beginning of the sample to drop. Used to reduce dependence on initial values.


Random sample(s) from an ARMA process.


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.ARIMA(y, (2, 0, 2), trend='n').fit(disp=0)
>>> model.params
array([ 0.79044189, -0.23140636,  0.70072904,  0.40608028])

Last update: Apr 12, 2024