feat: implement simulate method for sample trajectories

[ankitlade12]

Description

This PR significantly expands the simulate method capabilities across the StatsForecast library. Beyond providing basic sample trajectories, it now supports a wide range of error distributions, enabling high-fidelity probabilistic forecasting and robust scenario analysis.

This implementation centralizes simulation logic, improves model accuracy by incorporating historical residuals, and ensures high consistency across the model library.

Key Changes

• Advanced Error Distributions:
  • Introduced a centralized statsforecast/simulation.py utility for sampling from multiple distributions: normal, t (Student's t), bootstrap (empirical), laplace, skew-normal, and ged (Generalized Error Distribution).
  • Implemented calibrated variance scaling for all distributions to ensure generated noise matches the model's estimated sigma.
• Expanded Model Coverage:
  • Smoothing Models: Added simulate methods and analytic prediction intervals to SimpleExponentialSmoothing (Standard & Optimized) and SeasonalExponentialSmoothing (Standard & Optimized).
  • Averaging & Drift Models: Implemented simulate for HistoricAverage, RandomWalkWithDrift, and WindowAverage.
  • Stored Residuals: Updated fit methods across all models to calculate and store residuals and sigma, enabling non-parametric bootstrap simulation support.
• Improved API & Core Engine:
  • Enhanced StatsForecast.simulate and GroupedArray.simulate to propagate error_distribution and error_params through the hierarchy.
  • Full support for parallel execution (n_jobs) with reproducible seeding for all distributions.

Verification

• Automated Tests: Added tests/test_simulation_distributions.py covering:
  • High-level StatsForecast API simulations.
  • Individual model-level simulate implementations.
  • Reproducibility across seeds and parallel execution.
  • Bootstrap accuracy using historical residuals.
• Test Execution: Ran pytest tests/test_simulation_distributions.py — All 5 tests passed.

Checklist

• I have followed the Conventional Commits style for commit messages.
• I have added docstrings following the Google style.
• I have added tests to cover my changes.
• I have verified that all tests pass.
• I have run ruff to ensure compliance with the project's style.

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[MMenchero]

Thank you for your contribution @ankitlade12 We'll currently reviewing it and will get back to you soon.