EstemPMM News

Version 0.1.1 (2025-10-23)

Maintenance

• Updated DESCRIPTION (latest release date, Suggests list for packages used in the demos).
• Verified the package with R CMD check --as-cran (now warning-free after installing qpdf).
• Regenerated vignettes (HTML and tangled .R) and included them in inst/doc for distribution.
• Updated .Rbuildignore and .gitignore, keeping only files required for CRAN.

Version 0.1.0 (2025-01-15)

Initial Release: PMM2 Foundation

New Features: - lm_pmm2() - Linear regression estimation using Polynomial Maximization Method (S=2) - ar_pmm2() - Autoregressive (AR) time series modeling with PMM2 - ma_pmm2() - Moving Average (MA) time series modeling with PMM2 - arma_pmm2() - ARMA time series modeling with PMM2 - arima_pmm2() - ARIMA time series modeling with PMM2 - pmm2_inference() - Bootstrap inference for linear models - ts_pmm2_inference() - Bootstrap inference for time series models - Statistical utilities: pmm_skewness(), pmm_kurtosis(), compute_moments() - Comparison functions: compare_with_ols(), compare_ts_methods(), compare_ar_methods(), compare_ma_methods(), compare_arma_methods(), compare_arima_methods()

S4 Classes: - PMM2fit - Results container for linear regression models - TS2fit - Base class for time series results - ARPMM2, MAPMM2, ARMAPMM2, ARIMAPMM2 - Specialized time series result classes

Methods: - summary() - Model summary statistics - coef() - Extract coefficients - fitted() - Fitted values - predict() - Predictions for new data - residuals() - Model residuals - plot() - Diagnostic plots

Documentation: - Comprehensive Roxygen2 documentation for all exported functions - README with theoretical background and basic usage examples - Demonstration script pmm2_demo_runner.R showing practical applications

Package Architecture

Module Organization: - R/pmm2_main.R - Primary PMM2 fitting functions - R/pmm2_classes.R - S4 class definitions - R/pmm2_utils.R - Utility functions for moment computation and optimization - R/pmm2_ts_design.R - Time series design matrix construction

Dependencies: - Core: methods, stats, graphics, utils - Optional: MASS (for advanced statistical functions, available in Suggests)

Quality Assurance: - Unit tests covering core PMM2 functionality - Edge case handling for numerical stability - Convergence diagnostics and warnings

Known Limitations

• PMM2 only (S=2 order polynomial) - higher orders not yet implemented
• Single-stage estimation (no multi-stage procedures)
• Time series models assume stationarity for AR, MA components
• ARIMA differencing handled via preprocessing, not integrated into core algorithm

Roadmap for Future Versions

0.2.0 (PMM3 Ready Architecture): - PMM3 implementation (S=3 polynomial methods) - Refactored base classes supporting method extensibility - Vignette documentation with practical use cases - Enhanced bootstrap procedures for small samples - GitHub Actions CI/CD integration

0.3.0 (Advanced Methods): - Adaptive PMM order selection - Robust variance estimation - Model selection criteria (AIC/BIC for PMM) - Generalized Linear Models (GLM) with PMM

1.0.0 (Stable API): - API stabilization and backward compatibility guarantee - Extended performance benchmarks - Specialized applications (econometrics, biostatistics)

Citation

If you use EstemPMM in your research, please cite the relevant publications:

For Linear Regression (lm_pmm2): Zabolotnii S., Warsza Z.L., Tkachenko O. (2018) Polynomial Estimation of Linear Regression Parameters for the Asymmetric PDF of Errors. In: Szewczyk R., Zieliński C., Kaliczyńska M. (eds) Automation 2018. AUTOMATION 2018. Advances in Intelligent Systems and Computing, vol 743. Springer, Cham. https://doi.org/10.1007/978-3-319-77179-3_75

For Autoregressive Models (ar_pmm2): Zabolotnii S., Tkachenko O., Warsza Z.L. (2022) Application of the Polynomial Maximization Method for Estimation Parameters of Autoregressive Models with Asymmetric Innovations. In: Szewczyk R., Zieliński C., Kaliczyńska M. (eds) Automation 2022. AUTOMATION 2022. Advances in Intelligent Systems and Computing, vol 1427. Springer, Cham. https://doi.org/10.1007/978-3-031-03502-9_37

For Moving Average Models (ma_pmm2): Zabolotnii S., Tkachenko O., Warsza Z.L. (2023) Polynomial Maximization Method for Estimation Parameters of Asymmetric Non-gaussian Moving Average Models. In: Szewczyk R., et al. (eds) Automation 2023. AUTOMATION 2023. Lecture Notes in Networks and Systems, vol 630. Springer, Cham.

Technical Notes

Algorithm Stability: - Regularization parameter automatically adjusted for ill-conditioned systems - Step size limiting prevents divergence in optimization - Convergence history tracking for diagnostics

Numerical Considerations: - Moment estimation uses robust methods to handle outliers - Design matrices constructed with numerical stability in mind - NA/Inf values detected and handled appropriately