Correlation vs causation, causal inference and time-series concepts

Four ways a correlation misleads

Getting closer to causation

1. Randomised experiments (A/B tests) — the gold standard: randomisation balances confounders on average (previous lesson).
2. Difference-in-differences (DiD) — compare the change in a treated group with the change in a similar untreated group over the same period. Assumes the groups would have followed parallel trends without treatment.
3. Matched comparisons — compare treated units with untreated units that look similar on key characteristics (size, region, history).
4. Regression with controls — include known confounders as predictors; only as good as the confounders you measured.
5. Natural experiments / discontinuities — a rule creates as-good-as-random variation (e.g. eligibility cut-off).

Worked DiD example

A loyalty programme launched in Baku stores in March; other cities did not get it.

Naive before/after for Baku: +18. But stores elsewhere grew +10 in the same period (seasonality, general growth). DiD estimate = 18 − 10 = +8 per store-day — the effect attributable to the programme, if trends would otherwise have been parallel (check pre-period trends!).

Time-series concepts

A time series is a sequence of observations ordered in time. Typical components:

• Trend — long-run direction (growth of ~12% a year at Orion Retail).
• Seasonality — patterns repeating with a fixed period (December peaks, weekend effects).
• Cycles — longer, irregular ups and downs (economic cycles).
• Residual / noise — what remains.

import pandas as pd, numpy as np
orders = pd.read_csv("retail/orders.csv", parse_dates=["order_date"])
items = pd.read_csv("retail/order_items.csv")
items["rev"] = items["quantity"] * items["unit_price"] * (1 - items["discount_pct"])
rev = items.merge(orders[["order_id", "order_date", "status"]], on="order_id")
m = rev[rev.status == "completed"].groupby(rev.order_date.dt.to_period("M"))["rev"].sum()
trend = m.rolling(12, center=True).mean()
seasonal_index = (m / trend).groupby(m.index.month).mean()
print("Seasonal index by month (1.00 = average month):")
print(seasonal_index.round(2).to_string())
lag1 = m.autocorr(1); lag12 = m.autocorr(12)
print(f"autocorrelation lag 1 = {lag1:.2f}, lag 12 = {lag12:.2f}")

Seasonal index by month (1.00 = average month):
order_date
1     0.96
2     0.71
3     1.02
4     0.95
5     1.07
6     1.02
7     1.04
8     0.96
9     0.90
10    0.91
11    1.10
12    1.40
autocorrelation lag 1 = 0.46, lag 12 = 0.91

The seasonal index shows December about 40% above an average month and February almost 30% below — the pattern you saw in SQL. The 12-month moving average isolates the trend. Autocorrelation (correlation of a series with its own past values) is high at lag 12: this December resembles last December. That is useful for forecasting (seasonal naive forecasts exploit it) and dangerous for naive statistics (observations are not independent).

Practice

Summary

• Correlation can come from confounding, reverse causality, selection or coincidence.
• Experiments, DiD, matching and controls move analyses toward causal conclusions — each with assumptions to check.
• Time series = trend + seasonality (+ cycles) + noise; autocorrelation makes the past informative but breaks independence assumptions.