statsmodels.tsa.arima_process.arma_generate_sample¶
-
statsmodels.tsa.arima_process.
arma_generate_sample
(ar, ma, nsample, scale=1, distrvs=None, axis=0, burnin=0)[source]¶ Simulate data from an ARMA.
- Parameters
- ararray_like
The coefficient for autoregressive lag polynomial, including zero lag.
- maarray_like
The coefficient for moving-average lag polynomial, including zero lag.
- nsample
int
ortuple
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 unlessdistrvs
generates dependent data.- scale
float
The standard deviation of noise.
- distrvs
function
,random
number
generator A function that generates the random numbers, and takes sample size as argument. The default is np.random.randn.
- axis
int
See nsample for details.
- burnin
int
Number of observation at the beginning of the sample to drop. Used to reduce dependence on initial values.
- Returns
ndarray
Random sample(s) from an ARMA process.
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])