smooth

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hex-sticker of the smooth package for Python

Python implementation of the smooth package for forecasting and time series analysis using Single Source of Error (SSOE) state-space models.

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The package includes the following models:

  • ADAM - Augmented Dynamic Adaptive Model, uniting exponential smoothing, ARIMA and regression, implemented in the ADAM class.
  • ETS - Exponential Smoothing in the SSOE state space form, implemented in the ES class.
  • CES - Complex Exponential Smoothing with complex-valued smoothing parameters, implemented in the CES class (fixed seasonality type) and AutoCES class (automatic seasonality selection).
  • MSARIMA - Multiple seasonal ARIMA in state space form, implemented in the MSARIMA class (fixed orders) and AutoMSARIMA class (automatic order selection).
  • OM - Occurrence Model for intermittent demand, implemented in the OM class (plus OMG for the general two-component model and AutoOM for automatic type selection).
  • SMA - Simple Moving Average in state-space form (an AR(m) model with fixed coefficients), implemented in the SMA class with automatic order selection.

The package also provides standalone data generators that mirror R's sim.* family — sim_es, sim_ssarima, sim_ces, sim_gum, sim_sma, and sim_oes — plus a .simulate() method on fitted ADAM, OM, and OMG objects. See Simulation Functions.

All of these are implemented with the support of the following features:

  • Automatic components selection in ETS and forecasts combination
  • Explanatory variables
  • Multiple seasonal models (e.g. for high frequency data)
  • Advanced loss functions
  • Fine tuning of any elements of ADAM/ETS/ARIMA/Regression
  • A variety of prediction interval construction methods

Like the R version, the Python smooth depends on the greybox package for distributions, information criteria, regressor selection, and the LOWESS smoother. It is installed automatically as a dependency.

Installation

From PyPI (recommended):

pip install smooth

From source (development):

pip install "git+https://github.com/openforecast-org/smooth.git@master#subdirectory=python"

See the Installation Guide for platform-specific instructions.

System Requirements

If installing from source, this package requires compilation of C++ extensions. Before installing, ensure you have:

  • C++ compiler (g++, clang++, or MSVC)
  • CMake >= 3.25
  • Armadillo linear algebra library

Quick Example

import numpy as np
from smooth import ADAM

# Sample data
y = np.array([10, 12, 15, 13, 16, 18, 20, 19, 22, 25, 28, 30,
              11, 13, 16, 14, 17, 19, 21, 20, 23, 26, 29, 31])

# Fit ADAM model with additive error, no trend, no seasonality
model = ADAM(model="ANN")
model.fit(y)

# Generate forecasts
forecasts = model.predict(h=12)

# With seasonal component (monthly data, annual seasonality)
model = ADAM(model="ANA", lags=[1, 12])
model.fit(y)
forecasts = model.predict(h=12)

ADAMX — ADAM with Explanatory Variables

This also works with the exponential smoothing (ETSX) via the ES() class.

import numpy as np
from smooth import ADAM

# Simulate data where y depends on two external regressors
rng = np.random.default_rng(42)
n = 120
X = rng.standard_normal((n, 2))
y = 10 + 2 * X[:, 0] - 1.5 * X[:, 1] + rng.standard_normal(n)

# Fit ETSX(AAN) — use all regressors with fixed coefficients
model = ADAM(model="AAN", regressors="use")
model.fit(y, X)
print(model)           # shows fitted coefficients including xreg

# Forecast 12 steps ahead with future regressor values
X_future = rng.standard_normal((12, 2))
fc = model.predict(h=12, X=X_future)
print(fc.mean)

# Automatic variable selection (drops insignificant regressors)
model_sel = ADAM(model="AAN", regressors="select")
model_sel.fit(y, X)

# Adaptive (time-varying) regressor coefficients
model_adp = ADAM(model="AAN", regressors="adapt")
model_adp.fit(y, X)

X accepts a NumPy array or a pandas DataFrame (column names are preserved as regressor names). regressors controls treatment: "use" (fixed coefficients), "select" (stepwise selection via greybox), or "adapt" (ETS-style time-varying coefficients).

AutoMSARIMA — Automatic ARIMA Order Selection

AutoMSARIMA selects the best ARIMA orders automatically using information criteria, mirroring R's auto.msarima(). It fixes distribution="dnorm" and uses pure ARIMA (no ETS components).

import numpy as np
from smooth import AutoMSARIMA

# Monthly time series (e.g. AirPassengers, 144 observations)
y = np.array([
    112, 118, 132, 129, 121, 135, 148, 148, 136, 119, 104, 118,
    # ... remaining observations
], dtype=float)

# Automatic seasonal ARIMA — searches up to ARIMA(3,2,3)(3,1,3)[12]
model = AutoMSARIMA(lags=[1, 12])
model.fit(y)
print(model)   # AutoMSARIMA: ARIMA([p,P],[d,D],[q,Q])

# Reduce search space for speed
model = AutoMSARIMA(
    lags=[1, 12],
    ar_order=[2, 1],   # max AR: p≤2 at lag 1, P≤1 at lag 12
    i_order=[2, 1],    # max I:  d≤2 at lag 1, D≤1 at lag 12
    ma_order=[2, 1],   # max MA: q≤2 at lag 1, Q≤1 at lag 12
)
model.fit(y)
fc = model.predict(h=24)

CES — Complex Exponential Smoothing

CES and AutoCES mirror R's ces() / auto.ces(). CES uses complex-valued smoothing parameters to capture both the level and the "potential" of a series, covering four seasonality modes: "none", "simple", "partial", "full".

import numpy as np
from smooth import CES, AutoCES

y = np.array([
    112, 118, 132, 129, 121, 135, 148, 148, 136, 119, 104, 118,
    115, 126, 141, 135, 125, 149, 170, 170, 158, 133, 114, 140,
], dtype=float)

# CES with a fixed seasonality type
model = CES(seasonality="partial", lags=[1, 12], h=6, holdout=True)
model.fit(y)
print(model.model_name)         # e.g. "CES(partial)"
print(model.a_, model.b_)       # complex smoothing parameters
fc = model.predict(h=6)
print(fc.mean)

# AutoCES — select the best seasonality type by information criterion
auto = AutoCES(lags=[1, 12], h=6, holdout=True, ic="AICc")
auto.fit(y)
print(auto.best_model_.model_name)

Note: strict R-parity in the two-stage NLopt path requires nlopt>=2.10.0; older versions still fit, but the BOBYQA stage-1 trajectory may differ slightly from R.

Documentation

The pages below document the models and their Python classes:

  • ADAM — Augmented Dynamic Adaptive Model — unified ETS/ARIMA/regression framework
  • AutoADAM — Automatic ADAM with distribution and ARIMA order selection
  • ES — Exponential Smoothing (ETS) wrapper for ADAM
  • CES — Complex Exponential Smoothing (CES, AutoCES)
  • MSARIMA — Multiple Seasonal ARIMA (fixed orders) and automatic selection (AutoMSARIMA)
  • OM — Occurrence Model for intermittent demand (OM, OMG, AutoOM)
  • SMA — Simple Moving Average in state-space form with automatic order selection
  • Simulation Functions — sim_es, sim_ssarima, sim_ces, sim_gum, sim_sma, sim_oes, and the .simulate() method on fitted models

Book: Svetunkov, I. (2023). Forecasting and Analytics with the Augmented Dynamic Adaptive Model (ADAM). Chapman and Hall/CRC. Online: https://openforecast.org/adam/

See Also

About

smooth is developed and maintained by OpenForecast, a demand forecasting and inventory management consultancy. The package implements the methods we use in our consulting and teach in our training courses.

Project links

Data verified by PyPI on Aug 27, 2026
Data provided by the project maintainers, verified at the time the release was uploaded to PyPI.

Key dates

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Credits

Author: Ivan Svetunkov, Filotas Theodosiou, Leonidas Tsaprounis

Maintainer: Ivan Svetunkov

GitHub Statistics

Data verified by PyPI on Aug 27, 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

GNU Lesser General Public License v2 or later (LGPLv2+) (GNU LESSER GENERAL PUBLIC LICENSE)

Requires

Python >=3.11

Provides Extra

dev r parallel docs

Tags

forecasting time-series state-space exponential-smoothing ETS ARIMA ADAM occurrence-model intermittent-demand moving-average

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Attestations: Values shown here reflect the state when the release was signed and may no longer be current.

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This release

1.0.8 This release

14 files

1.0.7

14 files

1.0.6

14 files

1.0.5

14 files

1.0.4

16 files

1.0.3

17 files

1.0.2

17 files

1.0.1

17 files

1.0.0

17 files

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