Lesson 47: Time Series Analysis

What is Time Series Analysis?

Time series analysis involves analyzing data points collected over time to identify patterns, trends, and make predictions. Unlike traditional ML where data points are independent, time series data points are dependent on previous values, making temporal relationships crucial.

Time series data appears in many domains: stock prices, weather patterns, sales data, sensor readings, and more. Understanding how to analyze and forecast time series is essential for many real-world applications.

Time Series Data Structure
import pandas as pd
import numpy as np

# Create time series data
dates = pd.date_range('2024-01-01', periods=100, freq='D')
values = 100 + np.cumsum(np.random.randn(100))  # Trend + noise

ts_data = pd.Series(values, index=dates)
print("Time Series Data:")
print(ts_data.head())
print(f"\\nData points: {len(ts_data)}")
print(f"Date range: {ts_data.index[0]} to {ts_data.index[-1]}")

Key Components of Time Series

Time series can be decomposed into several components:

Trend: Long-term increase or decrease in the data
Seasonality: Regular patterns that repeat at fixed intervals (daily, weekly, yearly)
Cyclical: Irregular cycles without fixed periods
Noise/Random: Random variation that cannot be explained

Time Series Visualization
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

# Generate sample time series with trend and seasonality
dates = pd.date_range('2024-01-01', periods=365, freq='D')
trend = np.linspace(100, 150, 365)
seasonality = 10 * np.sin(2 * np.pi * np.arange(365) / 365.25 * 4)  # 4 cycles per year
noise = np.random.randn(365) * 5
values = trend + seasonality + noise

ts = pd.Series(values, index=dates)
print(f"Mean: {ts.mean():.2f}")
print(f"Std: {ts.std():.2f}")
print("Time series has trend, seasonality, and noise")

Time Series Forecasting Models

Various models are used for time series forecasting:

ARIMA (AutoRegressive Integrated Moving Average): Classic statistical model for stationary time series
LSTM/RNN: Deep learning models that capture long-term dependencies
Prophet: Facebook's forecasting tool that handles seasonality automatically
Exponential Smoothing: Weighted averages of past observations

Simple Time Series Forecasting with LSTM
from tensorflow import keras
from tensorflow.keras import layers
import numpy as np

# Prepare time series data for LSTM
def create_sequences(data, seq_length):
    X, y = [], []
    for i in range(len(data) - seq_length):
        X.append(data[i:i+seq_length])
        y.append(data[i+seq_length])
    return np.array(X), np.array(y)

# Sample time series
data = np.sin(np.arange(0, 100, 0.1)) + np.random.randn(1000) * 0.1
seq_length = 10
X, y = create_sequences(data, seq_length)

print(f"Input sequences shape: {X.shape}")
print(f"Target values shape: {y.shape}")
print("Ready for LSTM training!")

Preprocessing Time Series

Important preprocessing steps for time series:

Stationarity: Ensure data is stationary (constant mean and variance) using differencing
Normalization: Scale data to help model training
Handling Missing Values: Forward fill, interpolation, or removal
Feature Engineering: Create lag features, rolling statistics, time-based features

💡 Stationarity Importance

Many time series models assume stationarity. Use differencing (subtracting previous value) or log transformations to make non-stationary series stationary before modeling!

Practical Applications

Time series analysis is crucial for:

Financial Forecasting: Stock prices, currency exchange rates, economic indicators
Sales & Demand Forecasting: Retail sales, inventory management, supply chain
Weather Prediction: Temperature, rainfall, climate modeling
IoT & Sensors: Monitoring equipment, predictive maintenance
Web Analytics: Website traffic, user behavior patterns

Exercise: Time Series Forecasting

In the exercise on the right, you'll prepare time series data for forecasting, create sequences for LSTM training, and build a simple forecasting model. You'll learn how to structure temporal data for machine learning.

This hands-on exercise will help you understand the fundamental steps in time series forecasting.

Time Series Analysis