Time Series Analysis

  1. Descriptive Analysis and Decomposition
    1. Exploratory Data Analysis
      1. Summary Statistics
        1. Central Tendency
          1. Variability Measures
            1. Distribution Shape
            2. Time-Based Statistics
              1. Rolling Statistics
                1. Expanding Window Statistics
                  1. Seasonal Statistics
                  2. Pattern Identification
                    1. Visual Pattern Recognition
                      1. Trend Identification
                        1. Seasonal Pattern Detection
                      2. Time Series Components
                        1. Trend Component
                          1. Trend Estimation Methods
                          2. Seasonal Component
                            1. Additive Seasonality
                              1. Multiplicative Seasonality
                                1. Complex Seasonal Patterns
                                2. Cyclical Component
                                  1. Business Cycles
                                    1. Economic Fluctuations
                                      1. Long-Term Cycles
                                      2. Irregular Component
                                        1. Random Fluctuations
                                          1. Noise Characteristics
                                            1. Outliers and Anomalies
                                          2. Decomposition Models
                                            1. Additive Decomposition
                                              1. Multiplicative Decomposition
                                                1. Mixed Models
                                                  1. Pseudo-Additive Models
                                                  2. Decomposition Methods
                                                    1. Classical Decomposition
                                                      1. Moving Average Trend Estimation
                                                        1. Seasonal Index Calculation
                                                          1. Residual Extraction
                                                          2. X-11 and X-13-ARIMA-SEATS
                                                            1. Seasonal Adjustment Procedures
                                                              1. Model-Based Decomposition
                                                                1. Quality Diagnostics
                                                                2. STL Decomposition
                                                                  1. Seasonal and Trend Decomposition using Loess
                                                                    1. Parameter Selection
                                                                      1. Robustness Features
                                                                      2. Empirical Mode Decomposition
                                                                        1. Intrinsic Mode Functions
                                                                          1. Hilbert-Huang Transform
                                                                          2. Wavelet Decomposition
                                                                            1. Multi-Resolution Analysis
                                                                              1. Time-Frequency Decomposition
                                                                            2. Seasonal Adjustment
                                                                              1. Purposes of Seasonal Adjustment
                                                                                1. Adjustment Procedures
                                                                                  1. Quality Assessment
                                                                                    1. Interpretation of Adjusted Series

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                                                                                  2. Foundational Concepts and Data Preparation

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                                                                                  4. Stationarity and Unit Root Analysis