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Time Series & Forecasting

This course provides a comprehensive journey through Time Series Analysis and Econometrics, moving from fundamental statistical properties to advanced machine learning and nonlinear modeling.

It is structured into four primary pillars:

1. Foundations & Classical Modeling (Weeks 1–4)

The course begins by establishing the "rules" of time series. You'll dive into the concept of stationarity—understanding why a constant mean and variance are the bedrock of reliable forecasting.

  • Key Concepts: Weak vs. Strong Stationarity, ACF/PACF functions, and the decomposition of data into trend, seasonality, and noise.

  • Models: ARIMA and its seasonal counterpart, SARIMA, which are the workhorses for linear univariate forecasting.

2. Forecasting & Long-Memory Processes (Weeks 5–6)

Once the models are identified and estimated, the focus shifts to how well they actually predict the future.

  • Focus: Evaluation metrics like MAE and RMSE, and smoothing techniques (Exponential Smoothing) for data with less structure.

  • Advanced Twist: You’ll explore Fractional Integration (ARFIMA) and the Hurst Exponent, which deal with "long-memory" data where past events influence the series over very long periods—a concept frequently applied in high-frequency finance.

3. Multivariate & Structural Dynamics (Weeks 7–9)

Real-world economic variables rarely exist in a vacuum. This section looks at how multiple series interact.

  • Key Concepts: Cointegration and Error Correction Models (ECM)—essential for modeling variables that may drift apart in the short term but are tied together in the long run (like spot and futures prices).

  • Techniques: Vector Autoregressions (VAR), Granger Causality (to see if one variable predicts another), and Frequency Domain Analysis to view series as a sum of cycles.

4. Volatility, Nonlinearity & Machine Learning (Weeks 10–12)

The final leg of the course addresses the "messiness" of financial markets and complex systems.

  • Volatility: You’ll master ARCH and GARCH models, which are used to forecast "risk" rather than just the price.

  • Modern Approaches: The course concludes with Nonlinear Regimes (like Markov Switching) and a transition into modern Machine Learning and Neural Networks (RNNs/LSTMs), bridging the gap between traditional econometrics and data science.