Feature Engineering for Time Series

Forecasting models do not understand time the way humans do. They only understand numbers placed in columns.

Feature engineering is the process of translating time-related patterns into numerical signals that models can learn from.

In this lesson, we will take a real-world time series and carefully transform it into meaningful features — step by step, with clear visuals.

A Real-World Example

Assume you are forecasting daily electricity consumption for a city.

Electricity usage depends on:

• Day of the week
• Recent usage patterns
• Seasonal behavior

Our goal is to convert these ideas into usable features.

Raw Time Series

Below is a simulated daily electricity usage series. It contains:

• A slow upward trend
• Weekly usage patterns
• Random fluctuations

import numpy as np

np.random.seed(10)
days = np.arange(180)
trend = 0.15 * days
seasonal = 12 * np.sin(2 * np.pi * days / 7)
noise = np.random.normal(0, 3, size=180)

usage = 120 + trend + seasonal + noise

This is what most real-world data looks like — useful information is mixed together.

Why Feature Engineering Is Necessary

A machine learning model does not automatically know:

• What happened yesterday
• What usually happens on weekends
• Whether recent values are increasing or decreasing

We must explicitly provide that information.

Lag Features (Recent Memory)

Lag features represent past values of the series.

They answer questions like:

• What was usage yesterday?
• What was usage two days ago?

lag_1 = np.roll(usage, 1)
lag_7 = np.roll(usage, 7)

What this plot shows:

• Lag-1 follows the original series closely
• Lag-7 aligns with weekly patterns

These features give the model short-term and seasonal memory.

Rolling Statistics (Local Context)

Rolling features summarize recent behavior instead of single points.

They answer questions like:

• Is usage increasing lately?
• Is recent usage stable or volatile?

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

Rolling averages:

• Smooth short-term noise
• Reveal underlying direction

Models use this to understand local trends.

Calendar Features

Some patterns are driven by the calendar, not past values.

Examples:

• Weekdays vs weekends
• Workdays vs holidays

Below is a simple weekend indicator.

day_of_week = days % 7
is_weekend = (day_of_week >= 5).astype(int)

This feature helps the model learn:

• Usage behaves differently on weekends
• Patterns repeat weekly

Why These Features Work Together

Each feature captures a different aspect of time:

• Lag features → recent memory
• Rolling statistics → local behavior
• Calendar features → external structure

Together, they convert time into learnable signals.

Practice Questions

Key Takeaways

• Models do not understand time by default
• Feature engineering bridges that gap
• Good features often matter more than complex models

Next lesson: we will build more powerful lag-based features.