Time Series Analysis and Forecasting

  1. Classical Forecasting Models
    1. Naive and Simple Methods
      1. Naive Forecast
        1. Definition and application
          1. Seasonal naive forecast
            1. Performance characteristics
            2. Average Methods
              1. Simple average
                1. Moving average
                  1. Weighted moving average
                  2. Drift Method
                    1. Linear trend extrapolation
                      1. Parameter estimation
                      2. Strengths and Limitations
                        1. Computational simplicity
                          1. Benchmark performance
                            1. Lack of sophistication
                          2. Moving Average Models
                            1. Simple Moving Average
                              1. Definition and calculation
                                1. Window size selection
                                  1. Centered vs trailing averages
                                  2. Weighted Moving Average
                                    1. Weight selection strategies
                                      1. Exponential weights
                                      2. Double Moving Average
                                        1. Trend adjustment
                                          1. Brown's method
                                        2. Exponential Smoothing Models
                                          1. Simple Exponential Smoothing
                                            1. Model formulation
                                              1. Smoothing parameter estimation
                                                1. Initialization methods
                                                  1. Forecast intervals
                                                  2. Double Exponential Smoothing
                                                    1. Holt's linear trend method
                                                      1. Level and trend parameters
                                                        1. Damped trend models
                                                        2. Triple Exponential Smoothing
                                                          1. Holt-Winters method
                                                            1. Additive seasonality
                                                              1. Multiplicative seasonality
                                                                1. Parameter optimization
                                                                2. ETS Framework
                                                                  1. Error, Trend, Seasonal classification
                                                                    1. Model selection criteria
                                                                      1. Automatic model selection
                                                                    2. ARIMA Models
                                                                      1. Autoregressive Models
                                                                        1. AR(p) model specification
                                                                          1. Parameter estimation
                                                                            1. Stationarity conditions
                                                                              1. Characteristic equation
                                                                              2. Moving Average Models
                                                                                1. MA(q) model specification
                                                                                  1. Parameter estimation
                                                                                    1. Invertibility conditions
                                                                                    2. ARMA Models
                                                                                      1. Combined AR and MA components
                                                                                        1. Model identification
                                                                                          1. Parameter estimation
                                                                                          2. ARIMA Models
                                                                                            1. Integration component
                                                                                              1. Model notation ARIMA(p,d,q)
                                                                                                1. Differencing for stationarity
                                                                                                2. Box-Jenkins Methodology
                                                                                                  1. Model identification phase
                                                                                                    1. Parameter estimation phase
                                                                                                      1. Diagnostic checking phase
                                                                                                        1. Forecasting phase
                                                                                                        2. Seasonal ARIMA Models
                                                                                                          1. SARIMA notation
                                                                                                            1. Seasonal parameters
                                                                                                              1. Model building process
                                                                                                                1. Seasonal differencing
                                                                                                                2. Model Selection
                                                                                                                  1. Information criteria
                                                                                                                    1. Cross-validation
                                                                                                                      1. Residual analysis
                                                                                                                        1. Overfitting prevention

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                                                                                                                    4. Data Preprocessing and Exploration

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                                                                                                                    6. Advanced Statistical Models