GLS.fit().params contains only 1 value

[jmakov]

Describe the bug

I'm doing a linear fit with statsmodels.api.GLS. I stumbled upon a case where .fit() produces a result that has only 1 value in .params. I'd expect to get 2 - beta and the intercept (y=beta*x + intercept). I checked the docs, but sadly I'm no smarter. Am I perhaps using this incorrectly?

Code Sample, a copy-pastable example if possible

import statsmodels.api as sm

first_normalized_pc = pd.Series(...)
second_normalized_pc = pd.Series(...)

# get rolling difference
window_len = 100
differences = []
idx_start = 10000
idx_end = 40000

for i in range(idx_start, idx_end):
    window_end = i + window_len
    x = first_normalized_pc[i:window_end]
    S1 = sm.add_constant(x.values)
    y = second_normalized_pc[i:window_end]
    results = sm.GLS(y.values, S1).fit()
    differences.append(results.params[1] * x[-1] - y[-1] + results.params[0])

Expected Output

I'd naively expect that results.params contains 2 items.

Output of import statsmodels.api as sm; sm.show_versions()

INSTALLED VERSIONS

Python: 3.7.10.final.0
OS: Linux 5.4.0-89-generic #100-Ubuntu SMP Fri Sep 24 14:50:10 UTC 2021 x86_64
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8

statsmodels

Installed: 0.12.2 (/home/toaster/PROGS/miniconda3/envs/puma-lab/lib/python3.7/site-packages/statsmodels)

Required Dependencies

cython: 0.29.24 (/home/toaster/PROGS/miniconda3/envs/puma-lab/lib/python3.7/site-packages/Cython)
numpy: 1.20.3 (/home/toaster/PROGS/miniconda3/envs/puma-lab/lib/python3.7/site-packages/numpy)
scipy: 1.5.4 (/home/toaster/PROGS/miniconda3/envs/puma-lab/lib/python3.7/site-packages/scipy)
pandas: 1.3.2 (/home/toaster/PROGS/miniconda3/envs/puma-lab/lib/python3.7/site-packages/pandas)
dateutil: 2.8.2 (/home/toaster/PROGS/miniconda3/envs/puma-lab/lib/python3.7/site-packages/dateutil)
patsy: 0.5.2 (/home/toaster/PROGS/miniconda3/envs/puma-lab/lib/python3.7/site-packages/patsy)

Optional Dependencies

matplotlib: 3.4.3 (/home/toaster/PROGS/miniconda3/envs/puma-lab/lib/python3.7/site-packages/matplotlib)
backend: module://matplotlib_inline.backend_inline
cvxopt: Not installed
joblib: 1.0.1 (/home/toaster/PROGS/miniconda3/envs/puma-lab/lib/python3.7/site-packages/joblib)

Developer Tools

IPython: 7.27.0 (/home/toaster/PROGS/miniconda3/envs/puma-lab/lib/python3.7/site-packages/IPython)
jinja2: 3.0.1 (/home/toaster/PROGS/miniconda3/envs/puma-lab/lib/python3.7/site-packages/jinja2)
sphinx: Not installed
pygments: 2.10.0 (/home/toaster/PROGS/miniconda3/envs/puma-lab/lib/python3.7/site-packages/pygments)
pytest: Not installed
virtualenv: Not installed

[josef-pkt]

this got lost.

The most likely reason is that x is constant in a window. By default, add_constant does NOT add a constant if one already exists.

In general it's better to add a constant to the dataframe, because then add_constant will not be in the loop and it avoids an additional array copy.

add_constant has an option to add the constant even if one already exists. However, in that case there will be two columns in x with constant values. In this case parameters will not be identified and the estimate by OLS/WLS/GLS is a pinv regularized solution.