Rolling Window Features

Lag features give the model individual past values. But in real life, we rarely make decisions based on a single past day.

We usually think in terms of recent behavior:

• How has demand behaved over the last few days?
• Is usage consistently rising or falling?
• Is volatility increasing?

Rolling window features capture exactly this kind of thinking.

Real-World Context

We continue with the same example:

Daily electricity consumption of a city.

An energy planner rarely asks:

“What was usage exactly yesterday?”

Instead, they ask:

• What is the recent average?
• Is consumption becoming unstable?
• Are peaks getting stronger?

Rolling windows convert these questions into numerical features.

What Is a Rolling Window?

A rolling window takes a fixed number of past observations and summarizes them.

Common summaries:

• Rolling mean
• Rolling minimum / maximum
• Rolling standard deviation

Each window moves forward one step at a time.

Base Time Series

Here is our electricity usage series again.

import numpy as np

np.random.seed(7)
days = np.arange(180)
usage = 120 + 0.2*days + 15*np.sin(2*np.pi*days/7) + np.random.normal(0,4,180)

Rolling Mean (Smoothing Recent Behavior)

The rolling mean answers:

“On average, how high has usage been recently?”

This smooths out noise and highlights underlying movement.

window = 7
rolling_mean = np.convolve(usage, np.ones(window)/window, mode='valid')

What you should notice:

• Sharp noise is reduced
• Weekly pattern becomes clearer
• Trend is easier to see

Rolling mean helps the model focus on signal, not noise.

Rolling Standard Deviation (Volatility)

Average alone is not enough.

Sometimes the question is:

“Is usage becoming unstable?”

Rolling standard deviation measures recent variability.

rolling_std = [
  np.std(usage[i-7:i]) if i >= 7 else None
  for i in range(len(usage))
]

Interpretation:

• Higher values → unstable consumption
• Lower values → predictable behavior

This feature is crucial for detecting risk and uncertainty.

Rolling Min & Max (Recent Extremes)

Rolling minimum and maximum show recent boundaries.

They answer:

• How low has usage dropped recently?
• How high has it peaked?

rolling_min = [
  np.min(usage[i-7:i]) if i >= 7 else None
  for i in range(len(usage))
]

rolling_max = [
  np.max(usage[i-7:i]) if i >= 7 else None
  for i in range(len(usage))
]

This gives the model context about recent extremes, not just central tendency.

Why Rolling Features Are Powerful

• Summarize recent history
• Reduce noise sensitivity
• Improve stability of predictions

Tree-based models and boosting algorithms benefit enormously from rolling statistics.

Common Window Sizes

• 7 → weekly behavior
• 14 → bi-weekly trends
• 30 → monthly patterns

Window size should match real-world cycles.

Practice Questions

Key Takeaways

• Rolling windows summarize recent history
• Different statistics capture different behavior
• They are essential for robust forecasting

Next lesson: we’ll learn how to split time series data correctly for training and testing.