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The smooth package implements Single Source of Error (SSOE) state-space models for forecasting and time series analysis. It is available for both R (CRAN) and Python (PyPI, port in active development).

Navigation aids

• Glossary — terminology and overloaded names (ar vs ar_order vs AR vs "ar", ETS letters, state-component names).
• Roadmap — what is R-only or not yet ported to Python.
• R-Python-differences — numerical-parity status between the two implementations.
• Installation — installation instructions.
• Resources — academic references and DOIs.
• llms.txt — machine-readable index of every wiki page (markdown llms.txt spec, with full URLs).

Quick Links

• CRAN Package
• PyPI Package
• GitHub Repository
• ADAM Online Book

Forecasting functions

Function	R	Python	Description
ADAM	adam()	ADAM	Unified ETS + ARIMA + regression in SSOE form.
AutoADAM	auto.adam()	AutoADAM	Automatic distribution and ARIMA-order selection.
ES	es()	ES	Exponential Smoothing wrapper for ADAM.
CES	ces(), auto.ces()	CES, AutoCES	Complex Exponential Smoothing.
MSARIMA	msarima(), auto.msarima()	MSARIMA, AutoMSARIMA	Multiple Seasonal ARIMA.
SSARIMA	ssarima()	—	State Space ARIMA. R-only — see Roadmap.
GUM	gum()	—	Generalised Univariate Model. R-only — see Roadmap.
SMA	sma()	SMA	Simple Moving Average.
OM	om(), omg(), auto.om(), oes()	OM, OMG, AutoOM	Occurrence model for intermittent demand.

Utility

Function	R	Python	Description
msdecompose	msdecompose()	msdecompose()	Multiple seasonal decomposition.

Getting Started

Python

from smooth import ADAM, AutoADAM, ES, msdecompose

# Automatic ETS model selection
model = ADAM(model="ZXZ", lags=12)
model.fit(y)
forecasts = model.predict(h=12)

# Automatic distribution and ARIMA selection
model = AutoADAM(model="ZZZ", lags=[1, 12],
                 orders={"ar": 2, "i": 2, "ma": 2})
model.fit(y)

# Simple Exponential Smoothing
model = ES(model="ZXZ")
model.fit(y)

# Time series decomposition
result = msdecompose(y, lags=[12], type='additive')

R

library(smooth)

# Automatic model selection
model <- adam(y, model="ZXZ", lags=12)
forecast(model, h=12)

# Automatic distribution and ARIMA selection
model <- auto.adam(y, model="ZZZ",
                   orders=list(ar=2, i=2, ma=2, select=TRUE),
                   distribution=c("dnorm","dlaplace","ds"))

# Exponential Smoothing
model <- es(y, model="ZXZ", h=12)

ADAM is the entry point for most forecasting tasks. It provides unified ETS + ARIMA + regression, multiple seasonality, several error distributions, intermittent-demand handling, external regressors, and automatic selection.

Parameter pages (shared across functions)

Page	Parameters documented
Model-Specification	model, ETS taxonomy, automatic-selection codes
Orders-and-Lags	orders, lags, ar_order / i_order / ma_order
Loss-Functions	loss (likelihood, MSE, MAE, HAM, multi-step, LASSO, RIDGE, custom)
Bounds	bounds and stability conditions on smoothing parameters
Initialisation	initial (backcasting / optimal / two-stage / complete / provided)
Persistence	persistence (alpha, beta, gamma, delta), phi
Explanatory-Variables	formula, xreg, X, regressors
Model-Estimation	optimiser, IC, Hessian, advanced options

Method pages (extractors on fitted models)

Page	Methods documented
Fitted-Values-and-Forecasts	fitted, actuals, forecast / predict
Coefficients-and-Parameters	coef, confint, vcov, coefbootstrap
Residuals-and-Errors	residuals, rstandard, rstudent, rmultistep, multicov, outlierdummy
Likelihood-and-Information-Criteria	logLik, AIC / BIC / AICc / BICc, accuracy, pls
Model-Information	nobs, nparam, sigma, modelType, modelName, orders, lags
Visualisation-and-Output	print, summary, plot, xtable
Refitting-and-Reforecasting	reapply, reforecast
Scale-Model	sm — R-only (Roadmap)
Simulation-Functions	sim.* (R) / sim_* (Python) family and the .simulate() method on fitted models

Functionality matrix

Capability	Wiki page
Estimate ETS (fixed type)	ADAM, ES
ETS model selection (default pool)	ADAM, ES
ETS selection from a user-supplied pool	ADAM, ES
AIC-weighted combination of ETS forecasts	ADAM, ES
ADAMX (fixed regressors)	Explanatory-Variables
ADAMX (stepwise regressor selection)	Explanatory-Variables
ADAMX (adaptive — time-varying regressor coefficients)	Explanatory-Variables
Multiple seasonal ETS (e.g. daily + weekly)	ADAM, ES
Point forecasts (mean / median)	Fitted-Values-and-Forecasts
Prediction intervals (analytical / simulated / semiparametric)	Fitted-Values-and-Forecasts
Cumulative forecasts	Fitted-Values-and-Forecasts
ARIMA (fixed orders)	MSARIMA, ADAM
ARIMA (automatic order selection)	AutoADAM, MSARIMA
Multiple seasonal ARIMA	MSARIMA, ADAM
ETS + ARIMA combined	ADAM, AutoADAM
Advanced loss functions	Loss-Functions
Fixed error distribution	ADAM, ES
Automatic distribution selection	AutoADAM
Outlier detection (use all)	AutoADAM, ADAM
Outlier detection (stepwise)	AutoADAM, ADAM
Occurrence model (intermittent demand)	OM
Scale model (heteroscedasticity)	Scale-Model — R-only
Diagnostic plots	Visualisation-and-Output
Multi-step forecast errors	Residuals-and-Errors

Numerical equivalence

The R and Python implementations produce identical results to machine precision across most outputs (coefficients, log-likelihood, fitted values, residuals, forecasts, information criteria, and vcov / confint / summary for OM, OMG, and ADAM with initial="backcasting"). The remaining gap is on vcov for initial="optimal" / "two-stage" ADAM, at the finite-difference Hessian floor (~1e-3 relative). See R-Python-differences.