AIForecastTS v1.0.0: Scientific Framework for Time Series Resonance & Turbulence Analysis

1. Abstract

AIForecastTS is a high-performance scientific library designed to bridge the gap between classical signal processing and modern machine learning for time series forecasting.

v1.0.0 is a major release introducing:

• Harmonic-Gradient Resonance (HGR) v2.0 with confidence intervals, Bayesian resonance, and Welch spectral analysis
• AutoARIMA & Exponential Smoothing (ETS) models
• 3-Model Scientific Ensemble (Prophet + HGR + AutoARIMA) with auto weight optimization
• Walk-Forward Backtesting framework with multi-model comparison
• Professional Visualization module (forecast plots, residual diagnostics, component decomposition)
• Enhanced Analytics (outlier detection, confirmatory stationarity testing, data quality reports)
• Upgraded AI Agent with structured scientific reports via Google Gemini

2. Theoretical Framework

2.1. Harmonic-Gradient Resonance (HGR) v2.0

Traditional forecasting often fails by treating signal and noise as a monolithic entity. HGR operates on the principle of Dual-Component Decomposition:

Resonance Module (Deterministic Physics)

The Resonance module assumes that every time series contains underlying periodicities driven by systemic cycles.

• Spectral Identification: Uses Welch's method (robust) or FFT to map the series into the frequency domain.
• Harmonic Regression: Selects the top $K$ dominant frequencies with 2nd-order harmonics and reconstructs the signal: $$y_{res}(t) = \beta_0 t + \beta_1 t^2 + \sum_{i=1}^{K} \sum_{j=1}^{2} [a_{ij} \sin(j\omega_i t) + b_{ij} \cos(j\omega_i t)]$$
• v2.0: Bayesian Ridge option for probabilistic resonance estimation

Turbulence Module (Stochastic Dynamics)

The residuals from the Resonance module ($y - y_{res}$) represent "Turbulence" — the chaotic, non-linear interactions.

• Multi-scale rolling statistics (windows: 3, 5, 7)
• Rate of change and exponential weighted features
• Temporal weighting with auto-tuned XGBoost
• v2.0: Confidence intervals via residual bootstrap

2.2. Scientific Ensemble v2.0

The ensemble now combines 3 forecasting paradigms:

Component	Paradigm	Strength
Prophet	Bayesian	Trend & seasonality
HGR	Physics-based	Frequency decomposition
AutoARIMA	Statistical	Classical Box-Jenkins

Weight optimization uses 3D grid search on validation data. Falls back gracefully to 2-model ensemble if ARIMA fails.

2.3. AutoARIMA & ETS

• AutoARIMA: Automatic $(p,d,q)(P,D,Q,m)$ selection via stepwise AIC optimization (pmdarima)
• ETS: Holt-Winters with automatic seasonal period detection and parameter optimization

3. Architecture & Modules

3.1. Advanced Analytics (aiforecastts.analytics)

• DataProcessor:
  • Multiple missing value strategies (interpolate, ffill, bfill, mean, median, drop)
  • Outlier detection (IQR, Z-score, Modified Z-score) and treatment (clip, interpolate)
  • Confirmatory stationarity testing (ADF + KPSS) with diagnostic conclusion
  • Auto-differencing, normalization (MinMax, Z-score, Robust)
  • Data quality reports
• FeatureEngineer:
  • Multi-scale lag features with differences and pct_change
  • Rolling statistics with range, skewness, EWMA
  • Technical indicators (RSI, MACD, Bollinger Bands, Stochastic, ROC)
  • Cyclic calendar encoding (sin/cos for month, day-of-week, hour)
  • Fourier features for multiple seasonal periods
  • Correlation-based feature importance
• ModelEvaluator:
  • Metrics: MAE, RMSE, MAPE, SMAPE, R², MedAE, MaxError
  • Directional Accuracy, Theil's U statistic
  • Residual diagnostics (normality, autocorrelation, skewness)
  • Multi-model comparison tables

3.2. Backtesting (aiforecastts.backtesting)

• Walk-forward validation (expanding/sliding window)
• Configurable forecast horizon and step size
• Multi-model comparison backtesting
• Per-fold and aggregate performance metrics

3.3. Visualization (aiforecastts.visualization)

• Forecast plots with confidence intervals
• HGR component decomposition (Resonance + Turbulence)
• Multi-model comparison plots
• 4-panel residual diagnostics (residuals, histogram, Q-Q, ACF)
• Backtest performance charts

3.4. AI Research Agent (aiforecastts.agents)

Powered by Google Gemini, the agent generates structured scientific reports with:

• Executive Summary
• Trend & Stationarity Analysis
• Forecast Interpretation with component analysis
• Confidence assessment and risk factors
• Actionable recommendations

4. Installation

pip install aiforecastts

For development:

pip install aiforecastts[dev]

5. Quick Start

5.1. Basic HGR Forecasting

import pandas as pd
from aiforecastts import TimeSeriesResearch

df = pd.read_csv("data.csv", index_col='date', parse_dates=True)

research = TimeSeriesResearch(df, target_col='value', model_type='hgr')
results = research.run_full_analysis(steps=14, return_ci=True)

print(results['forecast'][['hgr_forecast', 'ci_lower', 'ci_upper']])
print(results['stationarity'])
print(results['data_quality'])

5.2. Scientific Ensemble (3-Model)

research = TimeSeriesResearch(df, target_col='value', model_type='ensemble')
results = research.run_full_analysis(steps=7, treat_outliers=True)

print(results['forecast'][['prophet', 'hgr', 'arima', 'ensemble_forecast']])
print(results['model_summary'])

5.3. Model Comparison

research = TimeSeriesResearch(df, target_col='value')
comparison = research.compare_models(model_types=['hgr', 'arima', 'ets'], steps=14)

print(comparison['comparison_table'])

5.4. Walk-Forward Backtesting

research = TimeSeriesResearch(df, target_col='value', model_type='hgr')
bt_results = research.backtest(forecast_horizon=7, step_size=7, expanding=True)

print(f"Overall RMSE: {bt_results['overall_metrics']['RMSE']}")
print(f"Folds: {bt_results['n_folds']}")

5.5. Multi-Model Backtest Comparison

bt_compare = research.backtest_compare(
    model_types=['hgr', 'arima'],
    forecast_horizon=7,
    step_size=7,
)
print(bt_compare['comparison'])

5.6. Visualization

from aiforecastts import ForecastPlotter

# Forecast plot with CI
ForecastPlotter.plot_forecast(
    actual=df['value'],
    forecast=results['forecast'],
    title="HGR Forecast with Confidence Intervals",
    show_last_n=60,
)

# Component decomposition
ForecastPlotter.plot_components(results['forecast'])

# Residual diagnostics
ForecastPlotter.plot_residual_diagnostics(y_true, y_pred)

# Backtest results
ForecastPlotter.plot_backtest_results(bt_results)

5.7. AI Agent Analysis

results = research.run_full_analysis(
    agent_query="Analyze the resonance-turbulence interaction and assess forecast stability.",
    api_key="YOUR_GEMINI_API_KEY",
    steps=7,
)
print(results['agent_report'])

5.8. Individual Model Usage

from aiforecastts import HarmonicGradientResonance, AutoARIMAModel, ExponentialSmoothingModel

# HGR with confidence intervals
hgr = HarmonicGradientResonance(top_k_frequencies=5, use_bayesian_resonance=True)
hgr.fit(df, 'value', auto_tune=True)
forecast = hgr.predict(steps=14, return_ci=True)
print(hgr.summary())

# AutoARIMA
arima = AutoARIMAModel(seasonal=True, m=7)
arima.fit(df, 'value')
forecast = arima.predict(steps=14, return_ci=True)

# Exponential Smoothing
ets = ExponentialSmoothingModel(trend='add', seasonal='add')
ets.fit(df, 'value')
forecast = ets.predict(steps=14)

6. API Reference

Models

Class	Description
HarmonicGradientResonance	HGR v2.0 with CI, Bayesian, auto-tune
ScientificEnsemble	3-model ensemble (Prophet + HGR + ARIMA)
AutoARIMAModel	Auto-tuned ARIMA via pmdarima
ExponentialSmoothingModel	Holt-Winters ETS

Analytics

Class	Description
DataProcessor	Cleaning, outliers, stationarity, normalization
FeatureEngineer	Lag, rolling, technical, Fourier features
ModelEvaluator	Metrics, diagnostics, model comparison

Tools

Class	Description
TimeSeriesResearch	Main pipeline orchestrator
Backtester	Walk-forward validation framework
ForecastPlotter	Professional visualization
AIForecastAgent	Gemini-powered analysis agent

7. What's New in v1.0.0

Breaking Changes from v0.3.x

• check_stationarity() now returns conclusion instead of is_stationary
• ScientificEnsemble now includes ARIMA by default (use include_arima=False for v0.3 behavior)

New Features

• HGR v2.0: Confidence intervals, Bayesian Ridge, Welch spectral, auto-tuning
• AutoARIMA and ETS model wrappers
• 3-model ensemble with 3D weight optimization
• Walk-forward backtesting with multi-model comparison
• Professional visualization (forecast, components, diagnostics, backtest)
• Outlier detection/treatment (IQR, Z-score, Modified Z-score)
• Confirmatory stationarity (ADF + KPSS)
• Data quality reports
• Enhanced feature engineering (Fourier, cyclic encoding, EWMA)
• Model save/load functionality
• Structured AI agent reports

8. Future Research Directions

• Integration of Quantum-inspired optimization for frequency selection
• Support for Multi-variate HGR (MV-HGR) to capture cross-series correlations
• Real-time streaming analytics for high-frequency turbulence monitoring
• Neural network hybrid (HGR + Transformer)
• Conformal prediction intervals

9. Citation

If you use this library in your research, please cite it as:

Tuan, T. A. (2025). AIForecastTS: A Scientific Framework for Time Series Resonance & Turbulence Analysis. GitHub Repository. https://github.com/tuanthescientist/aiforecastts

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Developed by Tran Anh Tuan - (AI Forecast) aiconsultant.org