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.

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.