User story: trend, seasonality, and 'is this Tuesday weird?'

The story

Daily sessions on the website have a clear weekly rhythm. Marcus needs to spot days that are unusually high or low after accounting for that rhythm.

Decomposition

import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.tsa.seasonal import seasonal_decompose

df = pd.read_csv("daily_sessions.csv", parse_dates=["date"]).set_index("date").sort_index()

decomp = seasonal_decompose(df["sessions"], model="additive", period=7)
decomp.plot()
plt.tight_layout()
plt.savefig("decomposition.png", dpi=150)

Anomaly flag

# Residual = actual - trend - seasonal
resid = decomp.resid.dropna()
std = resid.std()
df["expected"] = (decomp.trend + decomp.seasonal)
df["anomaly"]  = (resid.abs() > 2 * std)

anomalies = df[df["anomaly"]].sort_values("sessions", ascending=False)
print(anomalies)

Plot with anomalies highlighted

fig, ax = plt.subplots(figsize=(12, 4))
ax.plot(df.index, df["sessions"], lw=0.8)
ax.plot(df.index, df["expected"], lw=1.2, color="#217346", label="expected")
mask = df["anomaly"].fillna(False)
ax.scatter(df.index[mask], df["sessions"][mask], color="red", s=20, zorder=3, label="anomaly")
ax.legend()
plt.tight_layout()
plt.savefig("anomalies.png", dpi=150)