Python regenerating ARMA params using statsmodels

Question

I am trying to regenerate the ARMA parameters from statsmodel in python. The code I am using is:

from statsmodels.tsa.arima_process import arma_generate_sample
import statsmodels.api as sm
arparams = np.array([.75, -.25])
maparams = np.array([.65, .35])
arparams = np.r_[1, -arparams]
maparam = np.r_[1, maparams]
nobs = 250
np.random.seed(2014)
y = arma_generate_sample(arparams, maparams, nobs) #generate ARMA series
res = sm.tsa.arma_order_select_ic(y, ic=['aic', 'bic'], trend='nc')
z = sm.tsa.ARMA(y, (2,2)).fit()
print z.arparams
array([ 0.13178508,  0.08568388])

The regenerated AR params are not same as the one I started with. What am I doing wrong?

Answer 1

The logic of your code is all right. However, the variance of the parameters is high because nobs=250 is relatively low. Increase nobs and your parameters will converge toward the parameters you specified eventually.

import statsmodels.api as sm
import numpy as np

# Parameters.
ar = np.array([.75, -.25])
ma = np.array([.65, .35])

# Simulate an ARMA process.
np.random.seed(42)
y = sm.tsa.arma_generate_sample(
    ar=np.r_[1, -ar],
    ma=np.r_[1, ma],
    nsample=10000,
    sigma=1,
)

# Fit ARMA process on the simulates to check coefficients, ACF and PACF.
model = sm.tsa.ARMA(y, (2, 2)).fit(trend='c')

# Plot ACF and PACF of estimated model.
sm.tsa.graphics.plot_acf(y, lags=20, zero=True);
sm.tsa.graphics.plot_pacf(y, lags=20, zero=True);
model.summary()

Reference: McKinney, W., Perktold, J., & Seabold, S. (2011)