Package: EstemPMM 0.4.0

The Problem: When OLS Falls Short | Practical Implications | The Solution: Polynomial Maximization Method (PMM2) | Theoretical Foundation | Getting Started with EstemPMM | Example 1: Simple Linear Regression with Skewed Errors | Data Generation | Visualize Error Distribution | Model Fitting: PMM2 vs OLS | Bootstrap Inference for Variance Comparison | Example 2: Multiple Regression | Example 3: Polynomial Regression | Diagnostic Plots | Comparing PMM2 with OLS: Monte Carlo Evidence | When to Use PMM2 | Practical Recommendations | Next Steps | Summary | References

The Problem: When OLS and PMM2 Are Not Enough | Where Platykurtic Errors Arise | The Solution: PMM3 (Polynomial Maximization Method, S=3) | The Newton-Raphson Algorithm | Getting Started | Example 1: Simple Regression with Uniform Errors | Data Generation | Visualize Error Distribution | Automatic Method Selection | Fit PMM3 | Compare with OLS | Example 2: Three-Way Comparison (OLS vs PMM2 vs PMM3) | Example 3: Real Data Diagnostic — Auto MPG Horsepower | Fit Quadratic Model | Dispatcher Recommendation | Visualize the OLS Fit | Example 4: Real Data — Auto MPG (Linear, PMM2 Case) | Example 5: Multiple Regression | Example 6: No-Intercept Model | Interpreting the PMM3 Summary | Adaptive Mode | Diagnostic Plots | Utility Functions | Testing Symmetry | Computing Moments | Sixth-Order Cumulant | Variance Factor | When to Use PMM3 | Decision Workflow | Efficiency Summary (Monte Carlo Evidence) | Next Steps | References

Introduction | Load Package | Part 1: Seasonal Autoregressive (SAR) Models | Understanding SAR Models | Example: SAR(1,1)_12 with Monthly Data | Seasonal Patterns Visualization | Fitting SAR Models: PMM2 vs Classical Methods | Understanding PMM2 Efficiency | Residual Diagnostics | Part 2: Seasonal Moving Average (SMA) Models | Understanding SMA Models | Example: SMA(1)_4 with Quarterly Data | Quarterly Seasonal Pattern | Fitting SMA Models | SMA Convergence Behavior | Part 3: Monte Carlo Evidence for Seasonal Models | SAR Monte Carlo Comparison | Part 4: SARMA and SARIMA Models | SARMA(p,P,q,Q)_s Models | SARIMA Models with Differencing | Part 5: Model Comparison and Selection | Comparing Different Methods | Information Criteria for Model Selection | Part 6: Real-World Example - Airline Passengers | Modeling Strategy | Part 7: Practical Guidelines | When to Use Seasonal Models | Choosing Between Seasonal Models | PMM2 vs Classical Methods | Diagnostic Checklist | Part 8: Advanced Topics | Multiple Seasonal Periods | Seasonal Adjustment | Bootstrap Inference for Seasonal Models | Summary | References | Next Steps

Introduction | When PMM3 vs PMM2 vs OLS? | Setup | Part 1: AR Models with PMM3 | AR(1) with Uniform Innovations | Fit AR(1): PMM3 vs MLE | AR(2) Model | Part 2: MA Models with PMM3 | MA(1) Model | MA(2) Model | Part 3: ARMA Models | ARMA(1,1) Model | Diagnostic Plots | Part 4: ARIMA Models with Differencing | ARIMA(1,1,0) Model | Fit ARIMA(1,1,0) | ARIMA(1,1,1) Model | Part 5: Forecasting with PMM3 Models | Forecasting ARMA Models | Part 6: Method Selection with pmm_dispatch() | Part 7: Real-Data Example — DJIA 2002 | Analyze Innovation Properties | Fit AR(1) with All Three Methods | Part 8: Real-Data Example — WTI Crude Oil Prices | Innovation Analysis | Fit and Compare | Part 9: Adaptive Mode | Part 10: Model Comparison via AIC | Practical Guidelines | When to Use PMM3 for Time Series | Diagnostic Workflow | Computational Notes | Efficiency Summary | Available Functions | Next Steps | References

Introduction | Setup | Part 1: Autoregressive (AR) Models | AR(1) Model with Skewed Innovations | Estimate AR(1) Model: PMM2 vs CSS | AR(2) Model | Part 2: Moving Average (MA) Models | MA(1) Model | MA(2) Model | Part 3: ARMA Models | ARMA(1,1) Model | Diagnostic Plots for ARMA Models | Part 4: ARIMA Models with Differencing | ARIMA(1,1,1) Model | Fitting ARIMA Models | Part 5: Bootstrap Inference for Time Series | Part 6: Comparing Methods with Monte Carlo | Part 7: Prediction with Time Series Models | Practical Guidelines | When to Use PMM2 for Time Series | Model Selection Strategy | Computational Considerations | Summary Statistics: Efficiency Gains | Advanced Topics | Custom Innovation Distributions | Part 8: Seasonal Models (SAR and SMA) | Seasonal Autoregressive (SAR) Models | Seasonal Moving Average (SMA) Models | Comparing Seasonal Methods | Practical Applications of Seasonal Models | Conclusion | Next Steps | References

Introduction | Bootstrap Basics | The Bootstrap Principle | Setup | Part 1: Bootstrap for Linear Regression | Basic Example: Simple Linear Regression | Understanding Bootstrap Distributions | Part 2: Confidence Interval Methods | Percentile Method | Bias-Corrected (BC) Method | Comparison with OLS | Part 3: Hypothesis Testing | Testing Individual Coefficients | Testing Equality of Coefficients | Part 4: Bootstrap for Time Series Models | AR Model Bootstrap | ARMA Model Bootstrap | Part 5: Choosing Bootstrap Parameters | Number of Bootstrap Samples (B) | Parallel Bootstrap | Part 6: Diagnostic Checks | Convergence of Bootstrap Estimates | Bootstrap Distribution Visualization | Part 7: Practical Guidelines | When to Use Bootstrap for PMM2 | Common Pitfalls and Solutions | Part 8: Advanced Topics | Studentized Bootstrap | Block Bootstrap for Time Series | Summary | Best Practices Checklist | References | Next Steps