Running
from statsmodels.tsa.statespace.sarimax import SARIMAX
model = SARIMAX([1,2,3,4,5,6,7,8,9,10], order=(0,0,1)).fit(disp=False)
print(model.summary())
print(model.predict())
yields
SARIMAX Results
==============================================================================
Dep. Variable: y No. Observations: 10
Model: SARIMAX(0, 0, 1) Log Likelihood -27.378
Date: Thu, 10 Aug 2023 AIC 58.756
Time: 18:44:11 BIC 59.361
Sample: 0 HQIC 58.092
- 10
Covariance Type: opg
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
ma.L1 0.9996 495.167 0.002 0.998 -969.509 971.508
sigma2 11.0045 5454.459 0.002 0.998 -1.07e+04 1.07e+04
===================================================================================
Ljung-Box (L1) (Q): 6.51 Jarque-Bera (JB): 0.62
Prob(Q): 0.01 Prob(JB): 0.73
Heteroskedasticity (H): 13.60 Skew: -0.01
Prob(H) (two-sided): 0.06 Kurtosis: 1.78
===================================================================================
and the prediction
[0. 0.49999996 0.99999988 1.49999978 1.99999964 2.49999948
2.99999929 3.49999907 3.99999881 4.49999853]
The moving average coefficient is ~1, so that's good. But what is going on with the prediction? Why does it start at 0 and then go up by ~0.5 each step? Mechanically, what is statsmodels doing here?
I'd appreciate it if someone could show a "by-hand" calculation of how to think about the MA process in this scenario, like here: How does statsmodels calculate in-sample predictions in AR models?
I'm aware the time-series that I provided is not stationary, and I'm aware of this question: How Statsmodels predict ma process
