Why I got 'The computed initial AR coefficient

问题:

I generate some data like [1, 6, 1, 6, 1, 6] and add noises under normal distribution. I use arma_order_select_ic to select order. Then aic_min_order is used to fit the ARMA model. Sometime the model works well. But sometimes it raises ValueError.

ValueError: The computed initial AR coefficients are not stationary

Here is my code.

import statsmodels.api as sm
import numpy as np
x = [1 if i%2 == 0 else 6 for i in range(50)]
eta = np.random.normal(0, 0.01, 50)
x = x + eta
res = sm.tsa.stattools.arma_order_select_ic(x, ic=['aic']) 
print res.aic_min_order
model = sm.tsa.ARMA(x, res.aic_min_order).fit(disp = 0)
print model.predict(45, 55)

Do I miss something or ARMA don't fit this kind of data？

回答1:

ARMA is designed for stationary processes and by default imposes stationarity on the parameter estimates.

Your data is not stationary, i.e. it the lag polynomial has a seasonal unit root. The usual treatment is to use seasonal differencing or a deterministic seasonal pattern for example with dummy variables or splines.

Statsmodels has currently no automatic season detection and model selection, but SARIMAX can be used for seasonal integrated ARMA processes.