nirvana-quant: A Statistical and Econometric Framework for Multivariate Cyclical Time Series

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nirvana-quant is an open-source Python and C++ research framework for multivariate time-series econometrics, state-space filtering, directional network spillover modeling, and counterfactual panel reconstruction.

The library bridges classical econometric foundations (Vector Autoregressions, Diebold–Yılmaz connectedness, Kalman filters) with modern non-parametric methods (piecewise regression trees, Fisher Information regularization, and finite-sample Split Conformal Prediction).

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🚀 Interactive Notebook Demo (1-Click Run)

Test the complete end-to-end systemic risk pipeline across 27 commercial banks with interactive network graphs, SVD market decoupling, domino default contagion, and Basel IV macroprudential capital surcharge calibration:

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📊 Visualizations & Topological Risk Analytics

The engine extracts systemic interbank connections from multivariate asset price series:

Pairwise Spillover Intensity Heatmap (27x27)	Directed Systemic Risk Network Topology

Net Transmitter vs. Receiver Ranking	Hub vs. Authority Scatterplot

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⚡ Quickstart in 3 Lines

pip install nirvana-quant

import pandas as pd
from nirvana import NirvanaConnectedness

# Fit a TVP-VAR causal Kalman network model
model = NirvanaConnectedness(kalman_q=1e-3, kalman_r=1e-2, orthogonalize_market=True)
results = model.fit(df_asset_returns)

print(f"Total Connectedness Index (TCI): {results.total_connectedness_index:.2f}%")
print("Top Shock Transmitters:", results.top_transmitters[:5])
print("Top Shock Receivers:", results.top_receivers[:5])

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🔬 Core Methodological Modules

1. Harmonic Feature Mapping (nirvana.manifold)

• Maps multi-frequency cyclical signals (such as quarterly financial reporting and annual cycles) onto periodic manifold coordinates ($\mathbb{T}^2 = S^1 \times S^1$).
• Incorporates Discrete Fourier Transform (DFT) power spectral estimation to identify dominant frequencies empirically.

2. Causal State-Space Filtering & TVP (nirvana.kalman)

• Implements sequential Kalman state-space estimation with strictly causal updates (zero lookahead bias).
• Utilizes the Joseph-stabilized covariance formulation: $$P_t = (I - K_t H) P_{t|t-1} (I - K_t H)^T + K_t R K_t^T$$ to ensure positive semi-definiteness under ill-conditioned measurement environments.
• Employs Huber-type innovation bounds to limit sensitivity to fat-tailed shocks.

3. Regularized Piecewise Regression (nirvana.tree)

• Captures non-linear residual structures via bounded piecewise regression trees.
• Utilizes Fisher Information Matrix metrics and sample-margin density criteria to guide terminal-node pruning and mitigate finite-sample overfitting.

4. Directional Spillover & Network Topology (nirvana.network)

• Computes directional connectedness matrices via Vector Autoregressions (VAR) and Generalized Forecast Error Variance Decomposition (GFEVD, Koop–Pesaran–Potter).
• Employs Singular Value Decomposition (SVD) to isolate pervasive common market factors from idiosyncratic innovations.
• Evaluates Kleinberg graph centrality measures (Hub and Authority scores) to distinguish net transmitters from net receivers of shocks.

5. Counterfactual Panel Reconstruction (nirvana.multiverse)

• Implements counterfactual imputation for unbalanced historical panels (such as pre-listing asset periods).
• Evaluates sensitivity across structured simulation paths anchored on peer-group dynamics and macroeconomic benchmarks.
• Uses cubic Hermite transition polynomials ($3t^2 - 2t^3$) to ensure boundary continuity between reconstructed and observed sample periods.

6. Two-Stage Estimation & Conformal Prediction (nirvana.static, nirvana.proof)

• Combines parametric base estimators (OLS, Ridge, Lasso) with non-linear residual trees in a two-stage additive framework.
• Computes distribution-free prediction intervals via Split Conformal Prediction, satisfying finite-sample coverage guarantees: $$P\Big(Y_{n+1} \in [\hat{Y}{n+1} - q, \hat{Y}{n+1} + q]\Big) \ge 1 - \alpha$$

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🏛️ Domain Extensions (nirvana.domains)

Domain-specific structural parameters are maintained in modular extensions:

• banking: Empirical asset-scaling adjustments, exchange price-band limits, and interbank liquidity position mappings for systemic risk studies.
• cybersecurity: Directed network graph modeling for anomalous traffic flows and node centrality analysis.
• supply_chain: Multi-tier propagation models for inventory volatility and supplier dependency shocks.

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💻 C++ Implementation (nirvana_cpp/)

For low-latency execution and integration into compiled pipelines, the repository includes a self-contained C++20 header library:

• Header-only: #include <nirvana/nirvana.hpp>.
• Self-contained linear algebra routines (matrix decomposition, SVD, pseudoinverse) without mandatory external dependencies.
• Compatible with standard C++20 compilers (GCC 12+, Clang 15+, MSVC 19.30+).

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📦 Installation Options

From PyPI (Recommended)

pip install nirvana-quant

From GitHub

pip install git+https://github.com/yinyusi65/nirvana-quant.git

From Local Source

git clone https://github.com/yinyusi65/nirvana-quant.git
cd nirvana-quant
pip install -e .

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📖 Usage Examples

1. Two-Stage Regression with Conformal Prediction Intervals

import numpy as np
from nirvana import NirvanaTwoStageRegressor

# Cross-sectional sample
np.random.seed(42)
X = np.random.randn(120, 3)
y = 1.8 * X[:, 0] - 0.7 * (X[:, 1] ** 2) + np.random.randn(120) * 0.15

# Fit two-stage additive model
regressor = NirvanaTwoStageRegressor(base_estimator="ols", max_depth=4)
regressor.fit(X, y)

# Compute 95% conformal prediction intervals
y_pred, y_lower, y_upper = regressor.predict_interval(X, alpha=0.05)
print(f"Point Forecast: {y_pred[0]:.3f}, 95% Interval: [{y_lower[0]:.3f}, {y_upper[0]:.3f}]")

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👤 Authors & Maintainers

• yinyusi65

📄 License

This project is licensed under the GNU General Public License v3.0 - see the LICENSE file for details.