I want to configure parameters in the model with .fix_params() of statsmodels

Question

I'm building a SARIMAX model.

model = statsmodels.tsa.statespace.sarimax.SARIMAX(endog=y, order=[1,0,1], seasonal_order=[1, 1, 0, 10])

I wanted some parameters to be 0, since the p-value is greater than 0.05 I used fix_params() { https://www.statsmodels.org/devel/generated/statsmodels.tsa.statespace.sarimax.SARIMAX.fix_params.html#statsmodels.tsa.statespace.sarimax.SARIMAX.fix_params }

model.fix_params({'ma.L1': 0}).sumary()

and this is the result I got. 'SARIMAX' object has no attribute 'fix_params'

please help me

Answer 1

You need to call fit with the parameters fixed. This is done using fix_params as a context manager. First the unconstrained model.

from statsmodels.tsa.arima_process import ArmaProcess
from statsmodels.tsa.statespace.sarimax import SARIMAX
import numpy as np

# Simulate SARIMAX(1, 0, 1)x(1, 1, [], 10)
# AR: (1-L^10)(1-0.5L)(1-0.8L^10)
# MA: (1+0.6L)
np.random.seed(20220304)
ar = [0.5, 0, 0, 0, 0, 0, 0, 0, 0, 1.8, -0.9, 0, 0, 0, 0, 0, 0, 0, 0, -0.8, 0.4]
ma = [0.6]
ap = ArmaProcess.from_coeffs(ar,ma)
y = ap.generate_sample(4000)

model = SARIMAX(endog=y, order=[1,0,1], seasonal_order=[1, 1, 0, 10])
res = model.fit()
res.summary()

The estimates are pretty close to the parameters used to generate the sample.

                                      SARIMAX Results
===========================================================================================
Dep. Variable:                                   y   No. Observations:                 4000
Model:             SARIMAX(1, 0, 1)x(1, 1, [], 10)   Log Likelihood               -5574.986
Date:                             Fri, 04 Mar 2022   AIC                          11157.971
Time:                                     10:18:45   BIC                          11183.138
Sample:                                          0   HQIC                         11166.893
                                            - 4000
Covariance Type:                               opg
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
ar.L1          0.5258      0.016     31.888      0.000       0.493       0.558
ma.L1          0.5665      0.016     35.395      0.000       0.535       0.598
ar.S.L10       0.8070      0.009     87.185      0.000       0.789       0.825
sigma2         0.9547      0.021     45.938      0.000       0.914       0.995
===================================================================================
Ljung-Box (L1) (Q):                   0.04   Jarque-Bera (JB):                 3.46
Prob(Q):                              0.83   Prob(JB):                         0.18
Heteroskedasticity (H):               0.94   Skew:                            -0.04
Prob(H) (two-sided):                  0.26   Kurtosis:                         3.12
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).

Next, we use the fix_params with the with keyword to temporarily fix parameters and then call fit inside the context manager.

with model.fix_params({'ma.L1': 0}):
    con_res = model.fit()
con_res.summary()

These parameters differ since there is no MA.

                                      SARIMAX Results
===========================================================================================
Dep. Variable:                                   y   No. Observations:                 4000
Model:             SARIMAX(1, 0, 1)x(1, 1, [], 10)   Log Likelihood               -5929.452
Date:                             Fri, 04 Mar 2022   AIC                          11864.904
Time:                                     10:18:29   BIC                          11883.779
Sample:                                          0   HQIC                         11871.595
                                            - 4000
Covariance Type:                               opg
=================================================================================
                    coef    std err          z      P>|z|      [0.025      0.975]
---------------------------------------------------------------------------------
ar.L1             0.7409      0.011     68.937      0.000       0.720       0.762
ma.L1 (fixed)          0        nan        nan        nan         nan         nan
ar.S.L10          0.8087      0.009     88.918      0.000       0.791       0.826
sigma2            1.1404      0.025     44.983      0.000       1.091       1.190
===================================================================================
Ljung-Box (L1) (Q):                 256.27   Jarque-Bera (JB):                 1.90
Prob(Q):                              0.00   Prob(JB):                         0.39
Heteroskedasticity (H):               0.92   Skew:                            -0.05
Prob(H) (two-sided):                  0.11   Kurtosis:                         3.03
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).

Note that the restriction you are using reduces the model to an MA(0), so it would be better to respecify the model with a 0 in the MA lag length.

pure_ar_model = SARIMAX(endog=y, order=[1,0,0], seasonal_order=[1, 1, 0, 10])
pure_ar_res = pure_ar_model.fit()
pure_ar_res.summary()

These parameters match the estimates with the fixed parameter.

                                     SARIMAX Results
==========================================================================================
Dep. Variable:                                  y   No. Observations:                 4000
Model:             SARIMAX(1, 0, 0)x(1, 1, 0, 10)   Log Likelihood               -5929.452
Date:                            Fri, 04 Mar 2022   AIC                          11864.904
Time:                                    10:18:13   BIC                          11883.779
Sample:                                         0   HQIC                         11871.595
                                           - 4000
Covariance Type:                              opg
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
ar.L1          0.7409      0.011     68.937      0.000       0.720       0.762
ar.S.L10       0.8087      0.009     88.920      0.000       0.791       0.827
sigma2         1.1404      0.025     44.983      0.000       1.091       1.190
===================================================================================
Ljung-Box (L1) (Q):                 256.27   Jarque-Bera (JB):                 1.90
Prob(Q):                              0.00   Prob(JB):                         0.39
Heteroskedasticity (H):               0.92   Skew:                            -0.05
Prob(H) (two-sided):                  0.11   Kurtosis:                         3.03
===================================================================================