Add a `PeriodicFeatureExtractor`

[matthias-wende-frequenz]

What's needed?

For forecasting we have been using average load and production profiles.

Given a time series, we want a module that is able to calculate the item wise average of repeating time windows of the same size and the same sample-rate, possibly all having the same distance.

Example:

Consider the time series $T = [1,2,3,4,5,6,7,8,9,1]$ and a window a length $2$ with distance $2$ starting at the first position.

Hence we get the sub-series $t_1=[1,2], t_2=[5,6], t_3=[9,1]$ and therefore the average $$t_{avg}=[(1+5+9)/3, (2+6+1)/3] = [5, 3]$$

Note: A position could likewise be a timestamp in a usual time-series representation.

Proposed solution

We want to design such a module in a way such that it

• uses batches of data (most likely cached in memory)
• is designed to work together with the data structure defined here
• it should be able to run calculations on demand and memoize the result

Use cases

It's been used for calculating average load and production profiles certain days.
For example it could just calculate the average load of some consume of the last seven days as well as the average PV production of the last four Tuesdays.

Alternatives and workarounds

It's possible to run the calculation and update the mean on a data stream whenever a new sample arrives. However we plan on storing batches of data in any case, as this can be used as a feature for ml models, and thus calculating the averages from the batches seems obvious.
Additionally this option hasn't been further explored so far.

Additional context

We have had a use-case where we where looking at a full days averaged data plus a 15 minute margin. Thus we will need to add a margin for a window size in order to re-engineer this feature.

[mathias-baumann-frequenz]

We'll probably be able to use https://numpy.org/doc/stable/reference/generated/numpy.lib.stride_tricks.as_strided.html#numpy.lib.stride_tricks.as_strided for accessing arrays in strides in numpy

possilby helpful: https://numpy.org/doc/stable/reference/generated/numpy.mean.html

[matthias-wende-frequenz]

We need a margin around the window, such that we can say we want a specific load profile of a certain weekday +-15min. That would translate to the following parameters:

window_size = 1day
distance = 6days
margin = 15min

We could also consider introducing independent left and right margins.

Note: maybe we want padding (the one that goes to the outside)

[matthias-wende-frequenz]

possilby helpful: numpy.org/doc/stable/reference/generated/numpy.mean.html

Indeed useful. We can reshape the array into an 2 dimensional first and use the where array to select which values to include, i.e. leaf out all values that are not in any window or window margin. Using numpy's internal functions is likely faster then iterating over the values in python for calculating the mean.

[matthias-wende-frequenz]

Note: Average Time Series can be empty or a series of zeros because there is not enough data existing in the buffer or the buffer is full of NaN or in case the averaging calculation hasn't finished in time.

[matthias-wende-frequenz]

Should be able to calculate mean, standard deviation and polynomial coefficients.