Impulso

Bayesian Vector Autoregression (VAR) in Python.

Overview

impulso provides a modern, Pythonic interface for Bayesian Vector Autoregression modeling. Built on PyMC, it enables full posterior inference for VAR models with informative priors, structural identification, impulse response analysis, and forecast error variance decomposition.

Core Pipeline

The library follows an immutable, type-safe pipeline:

VARData → VAR.fit() → FittedVAR → .set_identification_strategy() → IdentifiedVAR

• VARData: Validated time series data (endogenous/exogenous variables + DatetimeIndex)
• VAR: Model specification (lags, priors, exogenous variables)
• FittedVAR: Reduced-form posterior estimates with forecasting capabilities
• IdentifiedVAR: Structural VAR with impulse responses, FEVD, and historical decomposition

Key Features

• Full Bayesian inference via PyMC (NUTS sampling, automatic diagnostics)
• Minnesota priors for regularization in high-dimensional VARs, with cross-lag scaling by relative variable scale (ADR-0015)
• Per-variable innovation priors: Override the innovation scale prior for individual variables
• Flexible identification schemes: Recursive (Cholesky), sign restrictions
• Forecasting: Point forecasts, credible intervals, and scenario analysis
• Impulse response functions (IRFs) with uncertainty quantification
• Forecast error variance decomposition (FEVD)
• Historical decomposition of variables into structural shocks
• Dynamic multipliers: Response of endogenous variables to exogenous (VARX) drivers
• Embeddable VARs: Build a VAR inside an existing PyMC model with VAR.build_in_model, with symbolic observed data or latent endogenous series generated in the model under a stationarity constraint, then wrap the posterior with FittedVAR.from_posterior (see ADR-0016)
• Extensible protocols: Plug in custom priors, samplers, and identification schemes
• Type-safe: Frozen Pydantic models with full type hints

Installation

pip install impulso

Or with uv:

uv pip install impulso

Faster sampling with nutpie

For significantly faster NUTS sampling, install with the optional nutpie backend:

pip install "impulso[nutpie]"

Or with uv:

uv add impulso --extra nutpie

When nutpie is installed, it is used automatically as the default sampler. You can also select the backend explicitly:

from impulso.samplers import NUTSSampler

sampler = NUTSSampler(nuts_sampler="nutpie")   # or "pymc"
fitted = var.fit(data, sampler=sampler)

Quick Start

import pandas as pd
from impulso import VARData, VAR

# Load your time series data
df = pd.read_csv("data.csv", index_col="date", parse_dates=True)

# Create validated VAR data
data = VARData.from_df(df, endog_vars=["gdp", "inflation", "interest_rate"])

# Specify and fit a VAR(4) model with Minnesota prior
var = VAR(lags=4, prior="minnesota")
fitted = var.fit(data)

# Generate forecasts
forecast = fitted.forecast(steps=12)
forecast.plot()

# Structural identification and impulse responses
identified = fitted.set_identification_strategy("cholesky")
irf = identified.impulse_response(steps=20)
irf.plot()

# Forecast error variance decomposition
fevd = identified.fevd(steps=20)
fevd.plot()

Documentation

Full documentation, tutorials, and API reference: https://impulso.quantclimate.com

Development

See AGENTS.md for development setup, testing, and contribution guidelines.

License

MIT License. See LICENSE for details.

Citation

If you use impulso in your research, please cite:

@software{impulso,
  author = {Pinder, Thomas},
  title = {impulso: Bayesian Vector Autoregression in Python},
  year = {2026},
  url = {https://github.com/QuantClimate/Impulso}
}