drvarma

Exact maximum-likelihood estimation, forecasting and diagnostics of multivariate VARMA (vector ARMA) models — in pure Python, with an optional compiled C engine for speed.

import numpy as np
from drvarma import Model, datasets

series = datasets.simulate_varma(phi=[np.diag([0.5, 0.4, 0.3])], sigma=np.eye(3),
                                 n=300, mu=[100., 50., 75.], seed=1,
                                 names=["A", "B", "C"])
m = Model(series, p=2, q=0, include_mean=True).fit()
print(m.phi, m.sigma, m.loglik)
levels, lo, hi = m.forecast(12, bands=True)     # + 95% bands
print(m.diagnostics())                          # Hosking Q, Jarque-Bera

drvarma fits a stationary Gaussian VARMA(p, q), Φ(B)(wₜ − μ) = Θ(B) aₜ, aₜ ~ N(0, Σ), by exact maximum likelihood (no conditional/back-forecasting approximation), and gives forecasts (+ error bands), impulse responses, variance decompositions, residual diagnostics and volatility.

What this provides. drvarma is a pure-Python implementation of Mauricio's exact-likelihood algorithm for multivariate VARMA (1995 JASA / 1997 AS 311): an innovations-form factorisation that evaluates the exact Gaussian likelihood directly on the VARMA form, without a state-space / Kalman filter, maximised by a faithful factored-BFGS quasi-Newton. Exact ML for VARMA is also available in Python through state-space methods (e.g. statsmodels' Kalman-filter VARMAX); what drvarma adds is a faithful port of this specific, non-Kalman algorithm — which, as far as we know, is not otherwise available in Python — together with the surrounding forecasting/IRF/FEVD/diagnostics toolkit. It runs with no compiled code; the optional C engine is only an accelerator.

Install

pip install drvarma                       # pure-Python (numpy + scipy)

Optional extras: drvarma[plots] (matplotlib + pyfug charts), drvarma[forecast-report] (HTML forecast reports), drvarma[c-engine] (build the CFFI C engine — needs GSL dev headers, ~10–100× faster but optional).

Features

  • Exact-ML estimation of stationary VARMA(p, q) for general dimension m, with mean, diagonal AR/MA/covariance restrictions, and optional Hannan–Rissanen two-step start.
  • Forecasting in original units: level, period and annual variation, each with standard errors and 95 % bands; plus fixed-parameter recursive (out-of-sample) forecasting.
  • Structural analysis: orthogonalised impulse responses, accumulated responses, long-run gain, and the forecast-error variance decomposition.
  • Diagnostics: Hosking multivariate portmanteau, multivariate Jarque–Bera, per-series ACF/PACF and two-sided cross-correlation (CCF).
  • Volatility: exponential-weight and moving-window residual covariance.
  • Transforms: Box-Cox + regular/seasonal differencing and harmonic deseasonalisation (with re-seasonalised forecasts).
  • I/O & reports: .inp reader/writer, C-format .out/.forecast/ .recursive text reports, an HTML forecast report per series, and matplotlib charts.

Everything runs with no compiled code. The optional CFFI engine wraps the validated drvarma C core and is bit-compatible with the pure-Python path on well-conditioned problems — an accelerator only. The numerical methods are tabulated below; see docs/DEVELOPER_GUIDE.md for the complexity discussion and a pure-Python vs hybrid vs C performance study.

Command line

drvarma IPC3 3 0 -mean -deseason auto -forecast 24        # writes IPC3.out, .forecast
drvarma IPC3 3 0 -mean -forecast 24 -html                # + HTML report per series
drvarma IPC3 3 0 -mean -estwin 200 -forecast 12          # recursive (.recursive)
drvarma IPC3 3 0 -mean -volexp 0.05 20 -volmov 20        # volatility (.volexp/.volmov)

<file>.inp in, text reports out. Flags: -mean -diagar -diagma -diagcov -m {1,2} -twostep -deseason [auto|force] -scale S -forecast H -html -estwin N -volexp [α w] -volmov [w] (λ, d, D come from the .inp header).

Documentation

Numerical methods

Algorithm Reference Used for
Exact Gaussian VARMA log-likelihood (innovations factorisation, not Kalman) Mauricio (1995) JASA; Mauricio (1997) AS 311 Exact likelihood (drvarma._as311)
Factored-BFGS quasi-Newton + Dennis–Schnabel line search Dennis & Schnabel (1983) ML optimisation (drvarma._qnewt.raxopt)
Concentrated objective f1ᵐ·f2 (σ² profiled, Σ = σ²·Q) Mauricio (1995) JASA §3 Conditioning; covariance / std errors
Hannan–Rissanen two-step Hannan & Rissanen (1982) VARMA start (-twostep)
Companion-form Lyapunov / autocovariances Mauricio (1997) AS 311 Stationary covariance, ψ-weights
Orthogonalised IRF & FEVD (Cholesky of Σ) Lütkepohl (2005) Structural analysis
Hosking multivariate portmanteau; multivariate Jarque–Bera Hosking (1980); Jarque & Bera (1980) Residual diagnostics
Exponential / moving-window conditional covariance — Volatility (drvarma.volatility)

Cross-references: Mauricio (2002, JTSA 23(4)) and Shea (1989, AS 242) are the other efficient exact-likelihood methods compared in the literature.

Authors and licence

drvarma is developed by David E. Guerrero and Arthur B. Treadway, based on the exact-likelihood algorithms designed and coded by José Alberto Mauricio.

Released under the GNU General Public License v2.0 or later (GPL-2.0-or-later) — see COPYING.

Project links

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Avatar for warriord from gravatar.com warriord

Credits

Author: David E. Guerrero

GitHub Statistics

Data verified by PyPI on Aug 10, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License expression

GPL-2.0-or-later
View SPDX License List

Requires

Python >=3.10

Provides Extra

c-engine plots forecast-report mcp test

Tags

VARMA vector ARMA time series forecasting multivariate exact maximum likelihood econometrics impulse response

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0.1.6 This release

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