Windows: rolling, expanding and ewm

The daily series

The orders become a series per day: the quantity ordered each day of the year. The resample("D") ensures a value for each day, including those without orders (which become zero in the sum):

import numpy as np
import pandas as pd

pd.set_option("display.width", 170)
pd.set_option("display.max_columns", 20)

pedidos = pd.read_csv("dados/pedidos.csv", parse_dates=["data_pedido"])
diaria = pedidos.set_index("data_pedido")["quantidade"].resample("D").sum()
print(len(diaria), int(diaria.sum()))

365 4365

`rolling`: the sliding window

The rolling(7) looks at the 7 last values at each position, and the aggregation (mean, sum, max...) calculates over them. The first 6 days do not have 7 values to look at, and remain NaN, unless you accept incomplete windows with min_periods:

media7 = diaria.rolling(7).mean()
print(int(media7.isna().sum()), int(diaria.rolling(7, min_periods=1).mean().isna().sum()))
print(media7.iloc[6:9].round(2).tolist())

6 0
[10.57, 9.0, 7.71]

With min_periods=1, the average of the first days uses what exists (the average of the 1st day is the value itself). It's a choice: it leaves fewer gaps, and the first averages are less reliable (fewer data behind).

The time window

With a date index, the window can be a period, and not a number of rows. This is what you want when there are missing days, because 7D always means "the last 7 consecutive days":

por_tempo = diaria.rolling("7D").sum()
print(int(por_tempo.isna().sum()), int(por_tempo.iloc[6]) == int(diaria.iloc[:7].sum()))

0 True

The same calculation in NumPy

The moving average in Pandas is exactly the sliding window you saw in chapter 28 of the NumPy course. You can check that both give the same result:

from numpy.lib.stride_tricks import sliding_window_view

valores = diaria.to_numpy(dtype=float)
manual = sliding_window_view(valores, 7).mean(axis=1)
print(bool(np.allclose(manual, media7.to_numpy()[6:])))

True

The advantage of Pandas is what comes with it: the date labels, the handling of gaps (min_periods), and the window by period.

`expanding` and `ewm`

The expanding calculates over everything up to this point: a cumulative, an average since the beginning. The ewm (exponential average) gives more weight to recent values, and therefore reacts more quickly to a change than the rolling:

acumulado = diaria.expanding().sum()
print(bool(acumulado.iloc[-1] == diaria.sum()), bool(acumulado.is_monotonic_increasing))

media_exp = diaria.ewm(span=7).mean()
print(round(float(media_exp.iloc[-1]), 2), round(float(media7.iloc[-1]), 2))

True True
9.93 11.0

The last two numbers are similar but different: both smooth, but the exponential gives more weight to recent days.

Window by group

Applying the window within each group returns a result with a double index (group and date), which does not align with the original table. The reset_index(level=0, drop=True) removes the group level:

por_canal = (
    pedidos.set_index("data_pedido")
    .groupby("canal")["quantidade"]
    .rolling("7D").sum()
)
print(por_canal.index.names)
por_canal = por_canal.reset_index(level=0, drop=True)
print(por_canal.index.names, len(por_canal) == len(pedidos))

['canal', 'data_pedido']
['data_pedido'] True

Compare with the past

The shift(7) brings the value from the same day of the previous week, which eliminates the effect of the day of the week (the first 7 days have no comparison). And the pct_change of the weekly series gives the variation from one week to another:

semana = diaria.resample("W").sum()
print(semana.pct_change().round(3).iloc[1:4].tolist())
print(int((diaria - diaria.shift(7)).isna().sum()))

[0.133, -0.044, 0.538]
7