drvarma
Exact maximum-likelihood estimation, forecasting and diagnostics of multivariate VARMA (vector ARMA) models — in Python, with the compiled C likelihood engine in the binary wheels.
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
The binary wheels carry the compiled engine (CPython 3.10–3.13 on Linux
x86_64/aarch64, glibc and musl, macOS arm64 and Windows x86_64);
drvarma._engine.engine_backend() says "c". Where no wheel fits, pip builds
the sdist, which needs a C compiler and the GSL headers; if the build or the
load fails, drvarma warns and runs the pure-Python path: the same results,
20–250× slower.
Optional extras: drvarma[plots] (matplotlib + pyfug charts),
drvarma[forecast-report] (HTML forecast reports). drvarma[c-engine] is kept
for old install lines and adds nothing: cffi is a dependency.
drvarma is the engine and has no assistant of its own. The MCP assistant for
VARMA systems is sima
(pip install sima-tseries), built on drvarma's ladder.
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:
.inpreader/writer, C-format.out/.forecast/.recursivetext reports, an HTML forecast report per series, and matplotlib charts.
Everything also runs with no compiled code. The CFFI engine of the binary
wheels 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
The ladder (0.2): fue's models as input
drvarma ES.pre FR.pre DE.pre 0 0 -diagcov -forecast 24 -estwin 216 -o diag # the univariates
drvarma ES.pre FR.pre DE.pre 1 0 -forecast 24 -estwin 216 -o var1 # + cross dynamics
drvarma -split IPC3.inp -mean -ar 1 -dir specs/ # the old multivariate .inp -> fue .inp
Each series keeps its fue model (Box-Cox, deterministic terms, differencing,
mean, ARMA factors) on the diagonal; p q are the cross orders. A diagonal
gate checks that the joint model reproduces the univariate ones and stops the
program if it does not. In Python: drvarma.ladder.Ladder(files, p, q).fit().
See docs/LADDER.md.
The multivariate .inp (deprecated since 0.2 / C 5.0)
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
docs/LADDER.md— the ladder: fue's models as input, the gate, forecasting, one format, and the parity with the C.docs/USER_GUIDE.md— install, API, CLI, worked examples.docs/INP_FORMAT.md— the.inpinput format (a precise, assistant-friendly spec for preparing inputs).docs/DEVELOPER_GUIDE.md— internals, algorithmic complexity from the literature, and the performance study.
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.
1 maintainer
Metadata
1 maintainer
Release files for drvarma 0.2.1
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