Time Series Analysis: ARIMA, Prophet, ML Forecasting

Introduction: Predicting the Future

Stock prices, weather temperatures, website traffic, energy consumption – all change over time. Time series data has a temporal dimension that traditional ML ignores!

Key Challenge: Past values influence future values. We need models that capture temporal dependencies.

Learning Objectives

• Understand time series components (trend, seasonality, noise)
• Master ARIMA models for forecasting
• Apply exponential smoothing
• Handle temporal cross-validation
• Build forecasting pipelines
• Evaluate forecast accuracy

1. Time Series Components

Decomposition

Any time series can be decomposed into:

1. Trend: Long-term increase or decrease
2. Seasonality: Regular patterns (daily, weekly, yearly)
3. Residual: Random noise

2. Simple Forecasting Methods

Moving Average

Exponential Smoothing

3. ARIMA Models

ARIMA(p, d, q): AutoRegressive Integrated Moving Average

• p: Order of autoregression (AR)
• d: Degree of differencing
• q: Order of moving average (MA)

AR (AutoRegressive)

MA (Moving Average)

4. Temporal Cross-Validation

Critical: Never shuffle time series data! Use forward chaining (walk-forward validation).

5. Forecast Evaluation Metrics

Key Takeaways

✅ Time series has temporal dependencies – order matters!

✅ Components: Trend + Seasonality + Residual

✅ ARIMA models: Flexible framework for time series forecasting

✅ Temporal CV: Use forward chaining, never shuffle

✅ Metrics: MAE, RMSE, MAPE for forecast accuracy

What's Next?

Next lesson: Reinforcement Learning Introduction – agents, rewards, and learning optimal policies!

Further Reading

Interactive Visualizations

• Forecasting: Principles and Practice (3rd ed.) — Hyndman & Athanasopoulos. Free, open-access textbook with R companion. Run the code in your browser.
• Distill — Visual Information Theory — neighbor topic; deepens your intuition for residuals and entropy.
• Facebook NeuralProphet — Live Demo — interactive time-series notebooks combining classical decomposition with deep learning.

Video Tutorials

• StatQuest — Time Series Forecasting Series (Josh Starmer).
• Rob Hyndman — Forecasting Lectures — author of Forecasting: Principles and Practice.

Papers & Articles

• Forecasting at Scale (Prophet paper) — Taylor & Letham, Facebook 2017. The model behind prophet.
• N-BEATS: Neural Basis Expansion Analysis for Time Series Forecasting — Oreshkin et al., ICLR 2020. Strong neural baseline.
• Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting — Lim et al., 2021. The state-of-the-art transformer for time series.
• Are Transformers Effective for Time Series Forecasting? — Zeng et al., AAAI 2023. The provocative paper that brought back simple linear baselines (DLinear).
• Chronos: Learning the Language of Time Series — Ansari et al., 2024. Foundation models for time series.

Documentation & Books

• Book: Forecasting: Principles and Practice — Hyndman & Athanasopoulos (free online).
• statsmodels — Time Series Analysis — Python's classical-stats workhorse.
• Nixtla statsforecast, neuralforecast — modern, fast forecasting libraries.
• Darts — unified Python API for classical + deep-learning time series models.