12. Time Series Analysis and Forecasting

📌 What is Time Series Analysis?

Time series analysis is a method for analyzing data that is collected over time. The goal is to understand patterns like trends, seasonality, and cycles — and use this information to make forecasts about future values.

Examples of time series data:

Stock prices

Weather data

Sales data

Website traffic

📌 Key Components of Time Series

Trend: Long-term increase or decrease in the data.

Seasonality: Repeating patterns at regular intervals (daily, monthly, yearly).

Cyclic Patterns: Long-term fluctuations not tied to season (e.g., economic cycles).

Noise (Residual): Random variation that cannot be explained by the above.

📌 Time Series Forecasting

Forecasting is the process of predicting future values based on historical time series data.

Popular Techniques for Time Series Forecasting

1. Statistical Methods

a. ARIMA (AutoRegressive Integrated Moving Average)

AR: Uses the dependency between an observation and a number of lagged observations.

I: Uses differencing to make the time series stationary.

MA: Uses the dependency between an observation and a residual error.

Example using Python (statsmodels):

python

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from statsmodels.tsa.arima.model import ARIMA

model = ARIMA(data, order=(1, 1, 1))

model_fit = model.fit()

forecast = model_fit.forecast(steps=10)

b. Exponential Smoothing (ETS)

Good for capturing trend and seasonality.

Simple Exponential Smoothing (SES)

Holt’s Linear Trend Method

Holt-Winters Seasonal Method

python

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from statsmodels.tsa.holtwinters import ExponentialSmoothing

model = ExponentialSmoothing(data, trend='add', seasonal='add', seasonal_periods=12)

fit = model.fit()

forecast = fit.forecast(10)

2. Machine Learning Models

a. Random Forest / Gradient Boosting

Use lag features as inputs.

Not ideal for long-term forecasting.

b. XGBoost, LightGBM

Perform well on structured time series datasets when you engineer the right features.

c. Neural Networks (Deep Learning)

LSTM (Long Short-Term Memory): Specialized RNNs for sequence data.

CNN + RNN hybrids, Transformer-based models for complex forecasting.

Important Steps in Time Series Analysis

1. Visualize the Data

python

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import matplotlib.pyplot as plt

plt.plot(data)

2. Check Stationarity

Use ADF Test (Augmented Dickey-Fuller)

Stationary data has constant mean and variance over time.

3. Differencing (if needed)

Used to remove trends and make the data stationary.

4. Decomposition

Break down the time series into trend, seasonal, and residual components.

python

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from statsmodels.tsa.seasonal import seasonal_decompose

result = seasonal_decompose(data, model='additive')

result.plot()

5. Feature Engineering for Machine Learning

Lag features

Rolling mean / std

Date/time parts (hour, day, month)

Seasonal indicators (weekend, holidays)

Evaluating Forecast Accuracy

Use metrics such as:

MAE (Mean Absolute Error)

RMSE (Root Mean Squared Error)

MAPE (Mean Absolute Percentage Error)

python

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from sklearn.metrics import mean_absolute_error, mean_squared_error

import numpy as np

mae = mean_absolute_error(actual, forecast)

rmse = np.sqrt(mean_squared_error(actual, forecast))

Best Practices

Train/Test Split: Use time-based splitting (not random).

Cross-Validation: Use TimeSeriesSplit instead of regular k-fold.

Handle Missing Data: Use forward fill, interpolation, or model-based imputation.

Use Domain Knowledge: Add relevant calendar or event-based features.

✅ Summary

Step Description

Visualize Plot and explore patterns in data

Decompose Understand trend and seasonality

Stationarity Check Ensure model assumptions hold

Model Selection Choose between statistical or ML models

Evaluate Forecast Use metrics like MAE, RMSE, MAPE

Iterate & Improve Tune models, add features, validate predictions

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