Quantitative Methods

  1. Advanced Statistical Methods
    1. Multivariate Analysis
      1. Multivariate Data Structure
        1. Data Matrices
          1. Distance Measures
            1. Euclidean Distance
              1. Manhattan Distance
                1. Mahalanobis Distance
              2. Principal Component Analysis
                1. Objectives
                  1. Mathematical Foundation
                    1. Eigenvalues and Eigenvectors
                      1. Component Extraction
                        1. Component Interpretation
                          1. Scree Plots
                          2. Factor Analysis
                            1. Exploratory Factor Analysis
                              1. Factor Extraction Methods
                                1. Factor Rotation
                                  1. Factor Interpretation
                                  2. Confirmatory Factor Analysis
                                    1. Model Specification
                                      1. Model Fit Assessment
                                      2. Comparison with PCA
                                      3. Cluster Analysis
                                        1. Hierarchical Clustering
                                          1. Agglomerative Methods
                                            1. Divisive Methods
                                              1. Linkage Criteria
                                                1. Dendrograms
                                                2. Non-hierarchical Clustering
                                                  1. K-means Clustering
                                                    1. K-medoids Clustering
                                                    2. Cluster Validation
                                                      1. Internal Measures
                                                        1. External Measures
                                                      2. Discriminant Analysis
                                                        1. Linear Discriminant Analysis
                                                          1. Assumptions
                                                            1. Discriminant Functions
                                                              1. Classification Rules
                                                              2. Quadratic Discriminant Analysis
                                                                1. Model Evaluation
                                                                  1. Classification Accuracy
                                                                    1. Cross-validation
                                                                2. Time Series Analysis
                                                                  1. Time Series Components
                                                                    1. Trend Component
                                                                      1. Trend Estimation
                                                                      2. Seasonal Component
                                                                        1. Additive Seasonality
                                                                          1. Multiplicative Seasonality
                                                                            1. Seasonal Indices
                                                                            2. Cyclical Component
                                                                              1. Business Cycles
                                                                                1. Identification Methods
                                                                                2. Irregular Component
                                                                                  1. Random Variation
                                                                                    1. Outliers
                                                                                  2. Time Series Decomposition
                                                                                    1. Classical Decomposition
                                                                                      1. X-11 Decomposition
                                                                                        1. STL Decomposition
                                                                                        2. Stationarity
                                                                                          1. Weak Stationarity
                                                                                            1. Strong Stationarity
                                                                                              1. Tests for Stationarity
                                                                                                1. Augmented Dickey-Fuller Test
                                                                                                  1. KPSS Test
                                                                                                  2. Differencing
                                                                                                    1. First Differencing
                                                                                                      1. Seasonal Differencing
                                                                                                    2. Autocorrelation Analysis
                                                                                                      1. Autocorrelation Function
                                                                                                        1. Partial Autocorrelation Function
                                                                                                          1. Ljung-Box Test
                                                                                                          2. Forecasting Methods
                                                                                                            1. Naive Methods
                                                                                                              1. Simple Naive
                                                                                                                1. Seasonal Naive
                                                                                                                2. Smoothing Methods
                                                                                                                  1. Simple Moving Average
                                                                                                                    1. Weighted Moving Average
                                                                                                                      1. Simple Exponential Smoothing
                                                                                                                        1. Holt's Method
                                                                                                                          1. Holt-Winters Method
                                                                                                                          2. ARIMA Models
                                                                                                                            1. Autoregressive Models
                                                                                                                              1. Moving Average Models
                                                                                                                                1. ARIMA Model Identification
                                                                                                                                  1. Parameter Estimation
                                                                                                                                    1. Model Diagnostics
                                                                                                                                      1. Forecasting
                                                                                                                                      2. Seasonal ARIMA Models
                                                                                                                                        1. Model Specification
                                                                                                                                          1. Parameter Estimation
                                                                                                                                        2. Forecast Evaluation
                                                                                                                                          1. Forecast Accuracy Measures
                                                                                                                                            1. Mean Absolute Error
                                                                                                                                              1. Mean Squared Error
                                                                                                                                                1. Mean Absolute Percentage Error
                                                                                                                                                2. Forecast Intervals
                                                                                                                                                  1. Model Comparison

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                                                                                                                                              3. Correlation and Regression Analysis

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                                                                                                                                              5. Computational Methods and Simulation