Time Series Analysis and Forecasting

  1. Fundamental Concepts
    1. Components of a Time Series
      1. Trend Component
        1. Definition and identification
        2. Seasonal Component
          1. Definition and characteristics
            1. Fixed seasonality
              1. Changing seasonality
                1. Seasonal patterns vs seasonal effects
                2. Cyclical Component
                  1. Definition and properties
                    1. Distinction from seasonality
                      1. Business cycles
                        1. Economic cycles
                        2. Irregular Component
                          1. Random fluctuations
                            1. Noise characteristics
                              1. Error terms
                            2. Additive and Multiplicative Models
                              1. Additive decomposition
                                1. Multiplicative decomposition
                                  1. Mixed models
                                    1. Choosing between models
                                    2. Stationarity
                                      1. Strict Stationarity
                                        1. Definition and mathematical formulation
                                          1. Properties and implications
                                          2. Weak Stationarity
                                            1. Definition and conditions
                                              1. Covariance stationarity
                                                1. Second-order stationarity
                                                2. Importance of Stationarity
                                                  1. Statistical inference requirements
                                                    1. Modeling assumptions
                                                      1. Forecasting implications
                                                      2. Consequences of Non-Stationarity
                                                        1. Spurious regression
                                                          1. Invalid statistical tests
                                                            1. Poor forecasting performance
                                                            2. Types of Non-Stationarity
                                                              1. Trend non-stationarity
                                                                1. Seasonal non-stationarity
                                                                  1. Variance non-stationarity
                                                                2. Tests for Stationarity
                                                                  1. Visual Methods
                                                                    1. Time plots
                                                                      1. Rolling statistics plots
                                                                        1. Seasonal subseries plots
                                                                        2. Statistical Tests
                                                                          1. Augmented Dickey-Fuller Test
                                                                            1. Kwiatkowski-Phillips-Schmidt-Shin Test
                                                                              1. Phillips-Perron Test
                                                                                1. Zivot-Andrews Test
                                                                                2. Interpreting Test Results
                                                                                  1. Null and alternative hypotheses
                                                                                    1. P-values and critical values
                                                                                      1. Test power and limitations
                                                                                    2. Autocorrelation Structure
                                                                                      1. Autocovariance Function
                                                                                        1. Definition and properties
                                                                                          1. Lag relationships
                                                                                          2. Autocorrelation Function
                                                                                            1. Definition and interpretation
                                                                                              1. Sample autocorrelation
                                                                                                1. Theoretical autocorrelation
                                                                                                  1. Confidence intervals
                                                                                                  2. Partial Autocorrelation Function
                                                                                                    1. Definition and calculation
                                                                                                      1. Interpretation and uses
                                                                                                        1. Sample partial autocorrelation
                                                                                                        2. Cross-Correlation Function
                                                                                                          1. Definition for multivariate series
                                                                                                            1. Lead-lag relationships

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                                                                                                        2. Mathematical Foundations

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                                                                                                        4. Data Preprocessing and Exploration