Time Series Analysis and Forecasting

  1. Model Evaluation and Validation
    1. Forecasting Horizons
      1. One-Step-Ahead Forecasting
        1. Point forecasts
          1. Interval forecasts
          2. Multi-Step-Ahead Forecasting
            1. Direct strategy
              1. Recursive strategy
                1. DirRec strategy
                  1. MIMO strategy
                2. Performance Metrics
                  1. Scale-Dependent Errors
                    1. Mean Error
                      1. Mean Absolute Error
                        1. Mean Squared Error
                          1. Root Mean Squared Error
                          2. Percentage Errors
                            1. Mean Percentage Error
                              1. Mean Absolute Percentage Error
                                1. Symmetric Mean Absolute Percentage Error
                                2. Scale-Independent Errors
                                  1. Mean Absolute Scaled Error
                                    1. Relative Root Mean Squared Error
                                    2. Distributional Accuracy
                                      1. Quantile loss
                                        1. Continuous ranked probability score
                                          1. Energy score
                                          2. Directional Accuracy
                                            1. Hit rate
                                              1. Directional symmetry
                                            2. Validation Strategies
                                              1. Hold-Out Validation
                                                1. Train-test split
                                                  1. Temporal ordering preservation
                                                  2. Cross-Validation Techniques
                                                    1. Time series cross-validation
                                                      1. Rolling forecast origin
                                                        1. Expanding window validation
                                                          1. Sliding window validation
                                                          2. Walk-Forward Analysis
                                                            1. Out-of-sample testing
                                                              1. Retraining frequency
                                                                1. Model updating strategies
                                                              2. Residual Analysis
                                                                1. Residual Properties
                                                                  1. Zero mean assumption
                                                                    1. Constant variance
                                                                      1. Independence assumption
                                                                        1. Normality assumption
                                                                        2. Diagnostic Tests
                                                                          1. Ljung-Box test
                                                                            1. Durbin-Watson test
                                                                              1. Breusch-Godfrey test
                                                                                1. ARCH test
                                                                                2. Visual Diagnostics
                                                                                  1. Residual plots
                                                                                    1. Q-Q plots
                                                                                      1. Histogram analysis
                                                                                        1. ACF of residuals
                                                                                      2. Model Selection
                                                                                        1. Information Criteria
                                                                                          1. Akaike Information Criterion
                                                                                            1. Bayesian Information Criterion
                                                                                              1. Hannan-Quinn Criterion
                                                                                              2. Cross-Validation Scores
                                                                                                1. Time series CV error
                                                                                                  1. Rolling window performance
                                                                                                  2. Forecast Accuracy Comparison
                                                                                                    1. Statistical significance tests
                                                                                                      1. Diebold-Mariano test
                                                                                                        1. Model confidence sets

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                                                                                                    9. Advanced Topics and Applications