01
Unit 1: Time Series Fundamentals and Decomposition
Time series components (trend, seasonality, cycle, irregular), Stationarity concepts (weak vs. strict stationarity), Trend estimation (moving averages, polynomial fitting, LOESS), Seasonal decomposition (classical, STL - Seasonal-Trend decomposition using Loess), Autocorrelation (ACF) and partial autocorrelation (PACF) analysis, Differencing and transformations for stationarity.
02
Unit 2: Classical Time Series Models
ARIMA models (p,d,q parameters, stationarity/invertibility conditions), Box-Jenkins methodology, Model identification (ACF/PACF interpretation), Parameter estimation (MLE, least squares), Model diagnostics (Ljung-Box test, residual analysis), SARIMA for seasonal data, Seasonal differencing and Fourier terms.
03
Unit 3: Exponential Smoothing and State Space Models
Simple exponential smoothing, Holt's linear trend method, Holt-Winters seasonal method, ETS framework (error, trend, seasonal components), Optimal smoothing parameters (MLE optimization), State space representation, Kalman filter for parameter estimation, Dynamic linear models and interventions.
04
Unit 4: Modern Machine Learning for Time Series
Feature engineering (lagged variables, rolling statistics, Fourier features), Tree-based methods (XGBoost/LightGBM with time series splits), LSTM/GRU networks for sequential forecasting, Transformer models (Temporal Fusion Transformer, Informer), Ensemble methods (statistical + ML hybrid models), Cross-validation strategies (purged, embargoed, walk-forward).
05
Unit 5: Advanced Topics and Production Systems
Multivariate time series (VAR, VEC models), Hierarchical forecasting (bottom-up, top-down, optimal reconciliation), Anomaly detection (isolation forest, autoencoders, statistical process control), Probabilistic forecasting (quantile regression, conformal prediction), Automated ML (AutoTS, sktime, Darts), Production deployment (MLOps for time series, concept drift detection).