DOC: Clarify output size in statsmodels.tsa.stattools.acf

[enricovara]

Autocorrelation output size is inconsistent using statsmodels.tsa.stattools.acf

The statsmodels.tsa.stattools.acf function returns nlags+1 values for the acf and confint return variables (because it includes the output at lag 0 (ie., acf=1)) but nlags values for the qstat and values return variables. I see this as needlessly confusing and easily fixed by making all outputs of size nlags or all of size nlags+1. If otherwise there is a reason for this, I'd love to be educated!

Code Sample, a copy-pastable example if possible

import statsmodels.tsa.stattools as smtsa
import numpy as np
x = np.random.randint(0,10,size=20)
acf, confint, qstat, pvalues = smtsa.acf(x, nlags=7, qstat=True, alpha=0.05)

print('len(acf)', len(acf))
print('len(confint)', len(confint))
print('len(qstat)', len(qstat))
print('len(pvalues)', len(pvalues))

Output

len(acf) 8
len(confint) 8
len(qstat) 7
len(pvalues) 7

Expected Output

len(acf) 7
len(confint) 7
len(qstat) 7
len(pvalues) 7

or

len(acf) 8
len(confint) 8
len(qstat) 8
len(pvalues) 8

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

[paste the output of import statsmodels.api as sm; sm.show_versions() here below this line]
INSTALLED VERSIONS

Python: 3.7.12.final.0
OS: Linux 5.4.104+ #1 SMP Sat Jun 5 09:50:34 PDT 2021 x86_64
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8

Statsmodels

Installed: 0.10.2 (/usr/local/lib/python3.7/dist-packages/statsmodels)

Required Dependencies

cython: 0.29.24 (/usr/local/lib/python3.7/dist-packages/Cython)
numpy: 1.19.5 (/usr/local/lib/python3.7/dist-packages/numpy)
scipy: 1.4.1 (/usr/local/lib/python3.7/dist-packages/scipy)
pandas: 1.1.5 (/usr/local/lib/python3.7/dist-packages/pandas)
dateutil: 2.8.2 (/usr/local/lib/python3.7/dist-packages/dateutil)
patsy: 0.5.2 (/usr/local/lib/python3.7/dist-packages/patsy)

Optional Dependencies

matplotlib: 3.2.2 (/usr/local/lib/python3.7/dist-packages/matplotlib)
backend: module://ipykernel.pylab.backend_inline
cvxopt: 1.2.7 (/usr/local/lib/python3.7/dist-packages/cvxopt)
joblib: 1.0.1 (/usr/local/lib/python3.7/dist-packages/joblib)

Developer Tools

IPython: 5.5.0 (/usr/local/lib/python3.7/dist-packages/IPython)
jinja2: 2.11.3 (/usr/local/lib/python3.7/dist-packages/jinja2)
sphinx: 1.8.5 (/usr/local/lib/python3.7/dist-packages/sphinx)
pygments: 2.6.1 (/usr/local/lib/python3.7/dist-packages/pygments)
pytest: 3.6.4 (/usr/local/lib/python3.7/dist-packages)
virtualenv: Not installed

[bashtage]

I think it is because the ACF is well defined for lag 0 (it is the variance) while the q-stat and its p-value are not defined for 0 lags. Docs could be improved.

[enricovara]

The ACF for lag 0 is 1 if I'm not mistaken, and is therefore trivial?

[bashtage]

Yes, sorry. Was thinking of autocov rather than autocorr. But still well defined. Of course, has no estimation error too. Probably not worth the pain to change these to match.

[enricovara]

I understand, thanks!

[bashtage]

I made a few smal changes in 7927, that build on your commits. Thanks for this.