# statsmodels.tsa.arima_process.ArmaProcess¶

class `statsmodels.tsa.arima_process.``ArmaProcess`(ar, ma, nobs=100)[source]

Represent an ARMA process for given lag-polynomials

This is a class to bring together properties of the process. It does not do any estimation or statistical analysis.

Parameters: ar : array_like, 1d Coefficient for autoregressive lag polynomial, including zero lag. See the notes for some information about the sign. ma : array_like, 1d Coefficient for moving-average lag polynomial, including zero lag nobs : int, optional Length of simulated time series. Used, for example, if a sample is generated. See example.

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 paramters 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, -ar] # add zero-lag and negate
>>> ma = np.r_[1, ma] # add zero-lag
>>> arma_process = sm.tsa.ArmaProcess(ar, ma)
>>> arma_process.isstationary
True
>>> arma_process.isinvertible
True
>>> y = arma_process.generate_sample(250)
>>> model = sm.tsa.ARMA(y, (2, 2)).fit(trend='nc', disp=0)
>>> model.params
array([ 0.79044189, -0.23140636,  0.70072904,  0.40608028])
```

Methods

 `acf`([nobs]) theoretical autocorrelation function of an ARMA process `acovf`([nobs]) theoretical autocovariance function of ARMA process `arma2ar`([nobs]) `arma2ma`([nobs]) `from_coeffs`(arcoefs, macoefs[, nobs]) Create ArmaProcess instance from coefficients of the lag-polynomials `from_estimation`(model_results[, nobs]) Create ArmaProcess instance from ARMA estimation results `generate_sample`([nsample, scale, distrvs, ...]) generate ARMA samples `impulse_response`([nobs]) get the impulse response function (MA representation) for ARMA process `invertroots`([retnew]) make MA polynomial invertible by inverting roots inside unit circle `pacf`([nobs]) partial autocorrelation function of an ARMA process `periodogram`([nobs]) periodogram for ARMA process given by lag-polynomials ar and ma

Attributes

 `arroots` Roots of autoregressive lag-polynomial `isinvertible` Arma process is invertible if MA roots are outside unit circle `isstationary` Arma process is stationary if AR roots are outside unit circle `maroots` Roots of moving average lag-polynomial