Advanced Time Series Forecasting: SARIMA, GARCH, Machine Learning

00:00 When ARIMA is not enough for forecasting 01:05 Regime change and failing forecast models 01:57 Linear forecasting limits in real series 02:45 SARIMA models for seasonal time series 03:35 How to identify and validate SARIMA 04:34 Regression with ARMA temporal errors 05:20 Distributed lag models for delayed effects 06:12 SARIMAX with exogenous variables 07:10 GARCH models for changing volatility 07:58 ARCH and GARCH estimation diagnostics 08:50 Volatility persistence and risk forecasting 09:41 Machine learning for nonlinear forecasting 10:33 Deep learning for temporal patterns 11:25 LLM and graph models for time series 12:22 Forecast error metrics: MSE, MAE, MAPE 13:10 Error metrics as forecasting loss functions 13:55 Temporal validation with rolling windows 14:46 Fair model comparison on future data 15:30 Overfitting in complex forecasting models 16:16 Forecasting limits and irreducible noise 17:01 Choosing the right forecasting extension Video description Advanced time series forecasting extends ARIMA when the data show seasonality, external drivers, changing volatility, nonlinear patterns, or relational structure. When should you choose SARIMA, SARIMAX, GARCH, machine learning, deep learning, or graph-based forecasting instead of staying with a simpler linear baseline? This video explains how each extension answers a specific modeling limitation. SARIMA adds seasonal dependence, SARIMAX combines exogenous variables with seasonal errors, regression with temporal errors separates external effects from autocorrelation, and GARCH models conditional variance when uncertainty changes through time. It also introduces machine learning and deep learning forecasting through sliding windows, convolutional models, LSTM networks, large language model adaptations, and graph-based spatiotemporal models. The lesson connects model choice with evaluation: forecast error metrics, loss functions, temporal validation, fair model comparison, overfitting, and irreducible noise. The goal is to choose complexity only when it improves future performance under realistic time-ordered validation.