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

docs/USER_GUIDE.md — install, API, CLI, worked examples.
docs/INP_FORMAT.md — the .inp input 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.

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drvarma 0.1.3

drvarma

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