statsmodels.tsa.arima_process.arma_generate_sample(ar, ma, nsample, sigma=1, distrvs=<built-in method randn of mtrand.RandomState object at 0x2ac643d45450>, 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 (default: 0)

to reduce the effect of initial conditions, burnin observations at the beginning of the sample are dropped


sample : array

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 paramters 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])

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