Applied Time Series

🕐 Applied Time Series: Teaching Machines to See the Future

Imagine you’re a weather wizard. You look at clouds from yesterday, today, and right now—then you predict tomorrow’s rain. That’s exactly what time series does with data!

🎯 The Big Picture

Time series is like reading a storybook where every page is a moment in time. We learn patterns from past pages to guess what happens next!

Think of it like this:

• 📈 Stock prices going up and down
• 🌡️ Temperature changing through seasons
• 🛒 How many ice creams a shop sells each day

Our Mission Today: Learn 4 super powers:

1. Feature Engineering - Finding hidden clues in time
2. Cross-Validation - Testing our predictions fairly
3. Forecasting Strategies - Different ways to peek into the future
4. Deep Learning - Teaching neural networks to understand time

🔧 Part 1: Time Series Feature Engineering

What Is It?

Feature engineering is like being a detective. You take raw time data and find hidden clues that help machines learn better!

Simple Example:

• Raw data: “Monday: 100 sales, Tuesday: 120 sales…”
• Hidden clues: “Weekends have MORE sales!” or “Sales go UP every month!”

The Key Features We Extract

1. Lag Features (Looking Backward)

Today's value depends on yesterday!

If yesterday = 100 sales
Then today might be ~100 sales too

lag_1 = value from 1 day ago
lag_7 = value from 1 week ago

Think of it like remembering what you ate yesterday to guess what you’ll want today!

2. Rolling Statistics (Moving Averages)

Average of last 7 days = rolling_mean_7

Day 1: 10
Day 2: 20
Day 3: 30
...
Day 7: 70

Rolling Mean = (10+20+30+...+70) / 7

It’s like looking at your average test score across the last few exams!

3. Date/Time Features

From a date like "2024-03-15":
- Month: 3 (March)
- Day of Week: 5 (Friday)
- Is Weekend: No
- Quarter: 1

These help the machine know: “Oh, it’s Friday! People buy more pizza on Fridays!”

4. Trend & Seasonality

graph TD
    A["Raw Data"] --> B["Trend Component"]
    A --> C["Seasonal Component"]
    A --> D["Residual/Noise"]
    B --> E["Going up or down over time?"]
    C --> F["Repeating patterns?"]
    D --> G[Random stuff we can't explain]

Real Life Example:

• 🏖️ Ice cream sales TREND up over years
• 🏖️ SEASONAL spike every summer
• 🏖️ Random days with unexpected sales = residual

🧪 Part 2: Time Series Cross-Validation

Why Is It Special?

In regular data, we can shuffle and pick random samples for testing. But with time series… we can’t peek at the future!

❌ Wrong Way: Randomly picking dates (you might train on 2024 and test on 2023!)

✅ Right Way: Always train on PAST, test on FUTURE

Types of Time Series Cross-Validation

1. Train-Test Split (Simple)

[=====TRAIN=====][==TEST==]
  Jan-Sep           Oct-Dec

Just cut the data at a point. Train on earlier, test on later.

2. Rolling Window (Walk-Forward)

Fold 1: [TRAIN][TEST]
Fold 2:   [TRAIN][TEST]
Fold 3:     [TRAIN][TEST]

Like a window sliding forward through time!

graph TD
    A["Fold 1"] --> B["Train: Jan-Mar"]
    B --> C["Test: Apr"]
    D["Fold 2"] --> E["Train: Feb-Apr"]
    E --> F["Test: May"]
    G["Fold 3"] --> H["Train: Mar-May"]
    H --> I["Test: Jun"]

3. Expanding Window

Fold 1: [T][test]
Fold 2: [TT][test]
Fold 3: [TTT][test]

Training set GROWS each time! You use ALL past data.

Which One to Choose?

🔮 Part 3: Forecasting Strategies

The Big Question

When predicting multiple steps ahead (like next 7 days), how do we do it?

Strategy 1: Recursive (Multi-Step)

Predict one step → Use that prediction → Predict next step

Day 1: Predict → Got 100
Day 2: Use 100 as input → Predict → Got 105
Day 3: Use 105 as input → Predict → Got 102
...

Pros: One simple model Cons: Errors pile up! 😬

graph TD
    A["Predict Day 1"] --> B["100"]
    B --> C["Predict Day 2"]
    C --> D["105"]
    D --> E["Predict Day 3"]
    E --> F["102"]

Strategy 2: Direct (One Model Per Step)

Train separate models for each future step!

Model 1: Predicts 1 day ahead
Model 2: Predicts 2 days ahead
Model 3: Predicts 3 days ahead
...

Pros: Each model is optimized for its step Cons: Need many models!

Strategy 3: DirRec (Hybrid)

Mix of both! Predict step 1, then use it WITH original data for step 2.

Strategy 4: MIMO (Multiple Input Multiple Output)

One model predicts ALL future steps at once!

Input: Last 7 days
Output: Next 7 days (all at once!)

Pros: Captures relationships between outputs Cons: More complex to train

Quick Comparison

🧠 Part 4: Deep Learning for Time Series

Why Deep Learning?

Traditional methods (ARIMA, etc.) are great, but they struggle with:

• Very long patterns
• Complex relationships
• Multiple variables

Neural networks can learn any pattern if given enough data!

The Star Players

1. RNN (Recurrent Neural Network)

The brain that remembers! It passes information from one step to the next.

Input → [RNN Cell] → Output
            ↑___|
         (memory loop)

Problem: Forgets long-term patterns 😢

2. LSTM (Long Short-Term Memory)

RNN’s smarter cousin! Has special “gates” to remember important things and forget unimportant things.

graph TD
    A["Input Gate"] --> D["Cell State"]
    B["Forget Gate"] --> D
    D --> C["Output Gate"]
    C --> E["Output"]

Real Example:

• “Remember that last Christmas had huge sales!”
• “Forget that random Tuesday with weird data.”

3. GRU (Gated Recurrent Unit)

Like LSTM but simpler! Fewer gates, faster training.

• LSTM: 3 gates
• GRU: 2 gates

Same idea, less complexity!

4. Transformer Models

The new superstar! Uses “attention” to look at ALL time steps at once.

"Hey, December 2022, you're VERY
important for predicting December 2024!"

Why Transformers Win:

• Can see far into the past
• Process everything in parallel (fast!)
• Powers models like ChatGPT!

Choosing Your Model

graph TD
    A["How much data?"] --> B{Lots of data?}
    B -->|Yes| C["Deep Learning"]
    B -->|No| D["Traditional Methods"]
    C --> E{Long patterns?}
    E -->|Yes| F["Transformer/LSTM"]
    E -->|No| G["Simple RNN/GRU"]

Simple Code Structure

# LSTM for Time Series
model = Sequential([
    LSTM(50, input_shape=(steps, features)),
    Dense(1)
])

# steps = how many past points
# features = how many variables
# Dense(1) = predict next value

🎉 Putting It All Together

Here’s how a real project flows:

graph TD
    A["Raw Time Data"] --> B["Feature Engineering"]
    B --> C["Create lag, rolling, date features"]
    C --> D["Split with Time Series CV"]
    D --> E["Choose Model: LSTM/Transformer"]
    E --> F["Pick Forecasting Strategy"]
    F --> G["Train & Validate"]
    G --> H["Predict the Future!"]

💡 Key Takeaways

🚀 You’ve Got This!

Time series might seem tricky, but remember:

1. Past tells the future - Extract good features from history
2. Test fairly - Always validate on future data
3. Choose wisely - Pick the right forecasting strategy
4. Go deep - Use neural networks for complex patterns

Now you’re ready to teach machines to see the future! 🔮✨