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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

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 .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.

Metadata

Release files for drvarma 0.2.0

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drvarma-0.2.0-py3-none-any.whl Python 3 none any Details
drvarma-0.2.0-cp313-cp313-win_amd64.whl CPython 3.13 CPython 3.13 Windows x86-64 Details
drvarma-0.2.0-cp313-cp313-musllinux_1_2_x86_64.whl CPython 3.13 CPython 3.13 Linux musl 1.2+ x86-64 Details
drvarma-0.2.0-cp313-cp313-musllinux_1_2_aarch64.whl CPython 3.13 CPython 3.13 Linux musl 1.2+ ARM64 Details
drvarma-0.2.0-cp313-cp313-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl CPython 3.13 CPython 3.13 Linux glibc 2.28+ x86-64, Linux glibc 2.24+ x86-64 Details
drvarma-0.2.0-cp313-cp313-manylinux_2_24_aarch64.manylinux_2_28_aarch64.whl CPython 3.13 CPython 3.13 Linux glibc 2.24+ ARM64, Linux glibc 2.28+ ARM64 Details
drvarma-0.2.0-cp313-cp313-macosx_14_0_arm64.whl CPython 3.13 CPython 3.13 macOS 14.0+ ARM64 Details
drvarma-0.2.0-cp312-cp312-win_amd64.whl CPython 3.12 CPython 3.12 Windows x86-64 Details
drvarma-0.2.0-cp312-cp312-musllinux_1_2_x86_64.whl CPython 3.12 CPython 3.12 Linux musl 1.2+ x86-64 Details
drvarma-0.2.0-cp312-cp312-musllinux_1_2_aarch64.whl CPython 3.12 CPython 3.12 Linux musl 1.2+ ARM64 Details
drvarma-0.2.0-cp312-cp312-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl CPython 3.12 CPython 3.12 Linux glibc 2.24+ x86-64, Linux glibc 2.28+ x86-64 Details
drvarma-0.2.0-cp312-cp312-manylinux_2_24_aarch64.manylinux_2_28_aarch64.whl CPython 3.12 CPython 3.12 Linux glibc 2.28+ ARM64, Linux glibc 2.24+ ARM64 Details
drvarma-0.2.0-cp312-cp312-macosx_14_0_arm64.whl CPython 3.12 CPython 3.12 macOS 14.0+ ARM64 Details
drvarma-0.2.0-cp311-cp311-win_amd64.whl CPython 3.11 CPython 3.11 Windows x86-64 Details
drvarma-0.2.0-cp311-cp311-musllinux_1_2_x86_64.whl CPython 3.11 CPython 3.11 Linux musl 1.2+ x86-64 Details
drvarma-0.2.0-cp311-cp311-musllinux_1_2_aarch64.whl CPython 3.11 CPython 3.11 Linux musl 1.2+ ARM64 Details
drvarma-0.2.0-cp311-cp311-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl CPython 3.11 CPython 3.11 Linux glibc 2.28+ x86-64, Linux glibc 2.24+ x86-64 Details
drvarma-0.2.0-cp311-cp311-manylinux_2_24_aarch64.manylinux_2_28_aarch64.whl CPython 3.11 CPython 3.11 Linux glibc 2.28+ ARM64, Linux glibc 2.24+ ARM64 Details
drvarma-0.2.0-cp311-cp311-macosx_14_0_arm64.whl CPython 3.11 CPython 3.11 macOS 14.0+ ARM64 Details
drvarma-0.2.0-cp310-cp310-win_amd64.whl CPython 3.10 CPython 3.10 Windows x86-64 Details
drvarma-0.2.0-cp310-cp310-musllinux_1_2_x86_64.whl CPython 3.10 CPython 3.10 Linux musl 1.2+ x86-64 Details
drvarma-0.2.0-cp310-cp310-musllinux_1_2_aarch64.whl CPython 3.10 CPython 3.10 Linux musl 1.2+ ARM64 Details
drvarma-0.2.0-cp310-cp310-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl CPython 3.10 CPython 3.10 Linux glibc 2.28+ x86-64, Linux glibc 2.24+ x86-64 Details
drvarma-0.2.0-cp310-cp310-manylinux_2_24_aarch64.manylinux_2_28_aarch64.whl CPython 3.10 CPython 3.10 Linux glibc 2.24+ ARM64, Linux glibc 2.28+ ARM64 Details
drvarma-0.2.0-cp310-cp310-macosx_14_0_arm64.whl CPython 3.10 CPython 3.10 macOS 14.0+ ARM64 Details

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Release history Release notifications | RSS feed

0.2.1

26 release files

This release

0.2.0 This release

26 release files

0.1.7

26 release files

0.1.6

26 release files

0.1.5

26 release files

0.1.4

26 release files

0.1.1

2 release files

0.1.0

2 release files

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