Module 1.1: Why Causal Inference Matters

What You'll Learn

1. What time series data is (if you're new to it)
2. The critical difference between correlation and causation
3. Why standard machine learning can't answer "why" questions
4. What makes time series causal inference special
5. When to use Tigramite

First: What is Time Series Data?

Time series = data measured over time, in order.

Examples you encounter daily:

• Stock prices (every minute/hour/day)
• Temperature readings (every hour)
• Your heart rate (every second)
• Website traffic (every day)
• Factory sensor readings (every minute)

What makes it special:

• The ORDER matters (yesterday comes before today)
• Values often depend on their past (today's temperature relates to yesterday's)
• This ordering helps us figure out what CAUSES what!

In this tutorial, we'll learn how to discover causal relationships in time series data.

The Ice Cream Murder Mystery

Here's a true statistical fact:

Does this mean ice cream causes drowning? Should we ban ice cream to save lives?

Of course not! Both are caused by a hidden third variable: summer heat.

This is called a spurious correlation - two things that move together but don't cause each other.

Let's See This in Action

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(42)

# Simulate 365 days
days = np.arange(365)

# Summer heat (the REAL cause) - peaks in summer
temperature = 20 + 15 * np.sin(2 * np.pi * days / 365 - np.pi/2) + np.random.randn(365) * 3

# Ice cream sales - CAUSED by temperature
ice_cream = 100 + 2 * temperature + np.random.randn(365) * 10

# Drowning deaths - ALSO caused by temperature (people swim more)
drowning = 5 + 0.1 * temperature + np.random.randn(365) * 1

# Plot the spurious correlation
fig, axes = plt.subplots(1, 3, figsize=(14, 4))

axes[0].scatter(temperature, ice_cream, alpha=0.5, c='coral')
axes[0].set_xlabel('Temperature')
axes[0].set_ylabel('Ice Cream Sales')
axes[0].set_title('Temperature → Ice Cream\n(TRUE CAUSE)')

axes[1].scatter(temperature, drowning, alpha=0.5, c='steelblue')
axes[1].set_xlabel('Temperature')
axes[1].set_ylabel('Drowning Deaths')
axes[1].set_title('Temperature → Drowning\n(TRUE CAUSE)')

axes[2].scatter(ice_cream, drowning, alpha=0.5, c='purple')
axes[2].set_xlabel('Ice Cream Sales')
axes[2].set_ylabel('Drowning Deaths')
axes[2].set_title('Ice Cream vs Drowning\n(SPURIOUS CORRELATION!)')

plt.tight_layout()
plt.show()

# Calculate correlation
corr = np.corrcoef(ice_cream, drowning)[0, 1]
print(f"Correlation between ice cream and drowning: {corr:.3f}")
print("Looks strong! But it's NOT causation.")

The Three Types of Relationships

Causal inference helps us figure out which one we're dealing with!

Why Standard ML Can't Help

Machine learning is great at prediction:

• "Given today's data, what will sales be tomorrow?"

But it CANNOT answer causal questions:

• "If we CHANGE the price, what will happen to sales?"
• "What is CAUSING our quality issues?"
• "Which variable should we INTERVENE on?"

The Key Difference

Why Time Series is Special

Time series data has a superpower for causal inference:

If yesterday's rain is correlated with today's flooding, we KNOW the direction:

• Rain yesterday → Flood today (possible cause)
• Flood today → Rain yesterday (impossible!)

This is called temporal precedence and it's why Tigramite works so well.

Example: Factory with Lagged Effects

# Example: Factory with lagged effects
np.random.seed(42)
T = 200  # 200 time steps

# Machine temperature (autocorrelated - depends on its own past)
machine_temp = np.zeros(T)
machine_temp[0] = 50
for t in range(1, T):
    machine_temp[t] = 0.8 * machine_temp[t-1] + np.random.randn() * 5

# Product quality - affected by temperature 2 steps ago!
quality = np.zeros(T)
for t in range(2, T):
    quality[t] = 80 - 0.5 * machine_temp[t-2] + np.random.randn() * 3

# Plot
fig, axes = plt.subplots(2, 1, figsize=(12, 6), sharex=True)

axes[0].plot(machine_temp, 'coral', linewidth=1)
axes[0].set_ylabel('Machine Temperature')
axes[0].set_title('Factory Time Series Data')

axes[1].plot(quality, 'steelblue', linewidth=1)
axes[1].set_ylabel('Product Quality')
axes[1].set_xlabel('Time Step')

plt.tight_layout()
plt.show()

print("Notice: Temperature spike causes quality drop with a 2-step lag")
print("This is what Tigramite can discover automatically!")

When to Use Tigramite

Use Tigramite when you have time series data and want to answer:

Real-World Applications

• Climate science: What drives temperature changes?
• Manufacturing: What causes quality defects?
• Finance: What factors drive stock prices?
• Healthcare: What affects patient outcomes?
• Energy: What causes consumption spikes?

Quick Quiz

Key Takeaways

1. Correlation ≠ Causation - Two things moving together doesn't mean one causes the other
2. Hidden confounders are everywhere - Always ask "What could be causing BOTH?"
3. ML predicts, causal inference explains - Different tools for different questions
4. Time series has an advantage - Time ordering helps identify causal direction
5. Tigramite is your tool for discovering causal relationships in time series