fue — Exact Maximum Likelihood for Univariate Time Series

fue is a Python implementation of the FUE/FUF estimation engine originally written in C by Arthur B. Treadway and David E. Guerrero, based on the algorithms designed and coded by José Alberto Mauricio. It fits ARMAX models with linear transfer-function interventions by exact maximum likelihood using the Ansley (1979) innovations form and the Mauricio (1997, AS 311) / Mauricio (1995, JASA) algorithms.

📖 Documentation: davidesg.github.io/fue-python — what the model is, the file contract, the formal tests with their critical values, how the port was verified against the published algorithms, and why the wheel. Five runnable examples in examples/.

Features

  • Exact ML estimation of ARIMA/SARIMA/ARMAX models (Box–Jenkins family)
  • Seasonal and non-seasonal AR/MA operators; regular and seasonal differencing
  • Linear transfer function interventions: impulse, step, ramp, Fourier harmonics, alternator, and arbitrary user-defined regressors
  • Fixed-frequency AR/MA factors (AR(2) with constrained spectral peak)
  • Box–Cox transformation with automatic back-transformation of forecasts
  • Multi-step forecasts with asymptotic prediction intervals
  • ASCII .out and .pre report output compatible with the C FUE binary
  • HTML forecast reports (requires jinja2)
  • CLI tools fue and fuf mirroring the C binaries

Installation

pip install fue                  # pure Python (numpy + scipy + matplotlib)
pip install "fue[report]"        # + HTML forecast reports (jinja2)
pip install "fue[pdf]"           # + PDF export (weasyprint)

Python 3.10+ required.

Quick start

import numpy as np
import fue

# Build a time series
data = np.array([...])   # monthly observations
ts = fue.TimeSeries(data, freq=12, start=(2002, 1), name="CPI")

# Specify an ARIMA(1,1,0)(1,0,0)_12 model with a log transform
m = fue.Model(ts,
              ar=[[0.3]],          # AR(1), initial value 0.3
              sar=[[0.2]],         # seasonal AR(1) at lag 12
              d=1,                 # one regular difference
              boxlam=0.0,          # log transform (Box–Cox λ=0)
              refactor=100.0)

result = m.fit()
print(result.sigma2, result.aic)
m.plot_residuals()

Load from a .inp file (fue format)

ts, m = fue.load("model.inp")
result = m.fit()
m.write_out("model.out")
m.write_pre("model.pre")

Forecast from a pre-estimated .inp file (fuf format)

ts, m = fue.load_fuf("forecast_model.inp")
fr = m.forecast_fuf(horizon=24)
print(fr.level)          # point forecasts in original units
print(fr.level_std)      # forecast standard deviations

Command-line interface

# Estimate a model and write .out / .pre
fue model_name [eml|aml] [chk|nochk] [-f horizon]

# Generate forecasts from a pre-estimated .inp file
fuf forecast_model

Numerical methods

Algorithm Reference Used for
Ansley (1979) innovations form Mauricio (1997) AS 311 Exact log-likelihood (elf_scalar)
Kalman filter (quick recursions) Mélard (1984) AS 197 Inner BFGS loop (flikam_scalar)
BFGS with Cholesky factor update Dennis & Schnabel (1983) ch. 9 Optimization (raxopt)
Scaled objective Π(x)/Π₀ Mauricio (1995) JASA §3 Numerical conditioning

Bug tracking

Bugs are tracked in-repo under bugs/ — one Markdown file per report (BUG-NNNN-slug.md) with a small frontmatter schema. A fix references the id in its commit, e.g. fix(forecast): BUG-0001 ….

fue-bug list                       # list reports (open marked with *)
fue-bug show BUG-0001              # print a report
fue-bug new "title" --component forecast   # file a new report
fue-bug check                      # validate all reports (runs in CI, tests/test_bugs.py)
fue-bug index                      # regenerate bugs/README.md

Authors and licence

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

Released under the GNU General Public Licence v2.0 or later (GPL-2.0-or-later). See COPYING for the full licence text.

Project links

Data verified by PyPI on Aug 13, 2026
Data provided by the project maintainers, verified at the time the release was uploaded to PyPI.

Key dates

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  • Released:
Latest release

1 maintainer

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Avatar for warriord from gravatar.com warriord

Credits

Author: David E. Guerrero

GitHub Statistics

Data verified by PyPI on Aug 13, 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

GPL-2.0-or-later

Requires

Python >=3.10

Provides Extra

c-engine dev pdf report

Tags

time series ARIMA ARMAX exact maximum likelihood Box-Jenkins

Classifiers

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