Trend, seasonality and events

01The problem

The depot manager has a feel for the patterns: "Saturdays are busy, Sundays are dead, December is mad, and everyone buys drinks before Eid." He's right, but feelings can't be put into a spreadsheet or a model. How much busier is Saturday? How mad is December? Is the month-end payday bump real or a story?

Every forecasting method, from the simplest to the most advanced, works by capturing these patterns. Measuring them first tells you which ones matter and gives you something to check every model against.

02The concept

The building blocks of a demand series

Measuring each one

• Trend: a 28-day or 365-day rolling average smooths the rest away.
• Seasonal profiles: average units by weekday, or by month, divided by the overall average, give seasonal indices (1.25 = 25% above average).
• Events: compare event days with similar non-event days.

Additive or multiplicative?

When December adds a percentage (say 30%) rather than a fixed number of units, and that percentage stays similar as sales grow, the pattern is multiplicative. That's typical of demand, and it's why many forecasts model the log of sales, as you did with rents in Machine Learning Fundamentals.

03Example

import pandas as pd
import numpy as np

base = "https://academy.cloudtechanalytics.com/datasets/demand/"
sales = pd.read_csv(base + "daily_sales.csv", parse_dates=["date"])
holidays = pd.read_csv(base + "holidays.csv", parse_dates=["date"])
malt = sales[sales["product"] == "Malt drink 330ml (24)"].set_index("date")
closed = malt.index.isin(holidays.loc[holidays["depot_closed"] == 1, "date"])
open_days = malt[~closed]

weekday_index = open_days.groupby(open_days.index.day_name())["units"].mean() / open_days["units"].mean()
weekday_index.reindex(["Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"]).round(2)

date
Monday       1.01
Tuesday      0.99
Wednesday    0.99
Thursday     1.03
Friday       1.13
Saturday     1.28
Sunday       0.56
Name: units, dtype: float64

Saturday sells about a quarter more than an average day, and Sunday about half. Now the year, the month-end payday effect and promotions:

month_index = open_days.groupby(open_days.index.month)["units"].mean() / open_days["units"].mean()
print("December index:", round(month_index[12], 2), "  January index:", round(month_index[1], 2))

payday = (open_days.index.day >= open_days.index.days_in_month - 2) | (open_days.index.day <= 2)
print("Payday days vs other days:", round(open_days.loc[payday, "units"].mean() / open_days.loc[~payday, "units"].mean(), 2))
print("Promotion days vs other days:", round(open_days.loc[open_days["on_promotion"] == 1, "units"].mean() / open_days.loc[open_days["on_promotion"] == 0, "units"].mean(), 2))

December index: 1.34   January index: 0.86
Payday days vs other days: 1.09
Promotion days vs other days: 1.44

December runs well above an average month and January below it; paydays and promotions each lift sales. These are rough measurements (a promotion in a slow month and one in a busy month are lumped together), but they show which patterns any forecast must capture.

04Walkthrough

1. Run the cells. Plot the 28-day rolling average (malt["units"].rolling(28).mean().plot()) to see the trend under the noise.
2. Measure the pre-Eid effect: average units in the 5 days before each Eid against the same weekdays two weeks earlier.
3. Compare December's index for the malt drink with detergent's. Which is more seasonal?
4. List the patterns in order of how much they matter for a weekly order.

05Practice

06Check your understanding