Rolling average in pandas using a Gaussian window

Question

I want to estimate the rolling average of a time series B using a Gaussian window. The equation to do this would correspond to

$$\tilde{B_{s}}(t_{n}) = \frac{1}{A_{s}} \sum_{t_{m}= t_{n}-3s}^{t_{n}+3s}B(t_{m})e^{-\frac{(t_{m} -t_{n})^{2}}{2s^{2}}}$$

where $$ A_{s} = \sum_{t_{m}= t_{n}-3s}^{t_{n}+3s}e^{-\frac{(t_{m} -t_{n})^{2}}{2s^{2}}}$$

I am aware that pandas has a an option for a gaussian window.

For example see https://stackoverflow.com/questions/27099555/gaussian-kernel-density-smoothing-for-pandas-dataframe-resample

However, I am not sure if it is equivalent to the version of Gaussian averaging that I am interested in using.

So my questions are:

In

hrly = pd.Series(hourly[0][344:468]) 
smooth = hrly.rolling(window=5, win_type='gaussian', center=True).mean(std=0.5)

1. Is the win_type='gaussian' going to give me the desired result?
2. What is the role of std=0.5?
3. If I wanted to do this using .apply() and use a manual function, how should the function be like?

Answer 1

1. Don't you really just want to convolve? Then I'd propose you do that.
2. std means standard deviation; that's the $\sigma$ ou usually see in the definition of the Gaussian. Its "width". In your formula, it looks like the $s$, but I'm not 100% sure your $A_s$ actually is the same as the usual Gaussian pre-factor. Check against the usual definition of the Gaussian!
3. that I don't know, but it's really not a signal processing, but a Pandas/Python programming "craft" question -> asking (searching, first) on Stackoverflow "How do I .apply a function manually" is probably a good idea.

Answer 2

1. Yes it does (See SciPy's Gaussian Window). Yet it won't filter the edges.
2. This is the $\sigma$ parameter in your equation.
3. It is better to use the built in tool in this case. It will be much faster. Just remember to handle the edges.