[Utils] _calculate_sigma has warning if series has 1 data point

[cparmet]

Hi! Issue Severity = None because now that I understand the warning, it's no problem! Please let me know any questions. And thanks all!

What happened + What you expected to happen

What happened

When I fit Naive() models to a dataframe consisting of series with 1 point each, I get intermittent warnings:
RuntimeWarning: invalid value encountered in double_scalars. sigma = sigma / n

The warning occurs once. If I fit a fresh model to the same data 50 times, the warning only occurs once. Execute the loop again, zero warnings. But restart kernel, the loop throws one warning.

What I expected to happen

Forecasts looked as expected given the algorithm, and a Naive forecast on a series with one data point seems acceptable. But the warning made me look for a bug in my code or invalid data. The warning occurs when Naive().fit() calls _calculate_sigma(). I could see how we might get a divide by 0 or NaN issue in a standard deviation, but the intermittent nature of the warning was confusing, since this is a deterministic model fit to the same dataset.

From discussion with José on Nixtla Slack:

• The issue is indeed from fitting Naive() to a series with only 1 data point. After the chat I understood how the n passed to _calculate_sigma() is the series length - 1, so with my dataset n=0, and sigma / n divides by zero, throwing the warning.
• The intermittency appears to be related to the warnings module, but the divide by zero occurs every time.

José's suggestion:

We should probably change that so that if n is zero sigma is 0 or similar. Can you open an issue for that?

Versions / Dependencies

statsforecast 1.5.0 and 1.6.0
A Python 3.8 image on SageMaker

Also reproduced in Colab with Python 3.10.12, statsforecast 1.6.0

Reproduction script

# !pip install pandas statsforecast==1.6.0 # if running in notebook
import pandas as pd
from statsforecast import StatsForecast
from statsforecast.models import Naive

X = pd.DataFrame({'unique_id':[0,1,2,3,4], "ds":[1,1,1,1,1], "y":[10,20,30,40,50]})

naive_model = StatsForecast(models = [Naive()],
                            freq = 'MS',
                            n_jobs = 1)
naive_model.fit(X)

# Output
# /usr/local/lib/python3.10/dist-packages/statsforecast/utils.py:349: RuntimeWarning: invalid value encountered double_scalars
#  sigma = sigma / n  
# StatsForecast(models=[Naive])

Issue Severity

None