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smooth Wiki

Welcome to the smooth package wiki! The smooth package implements Single Source of Error (SSOE) state-space models for forecasting and time series analysis, available for both R and Python (under development).

Quick Links

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

Main Forecasting Functions

Function	Description	Python	R
ADAM	Augmented Dynamic Adaptive Model - unified ETS/ARIMA/regression framework	Yes	Yes
auto.adam	Automatic ADAM with distribution and ARIMA order selection	TBA	Yes
ES	Exponential Smoothing (ETS) wrapper for ADAM	Yes	Yes
CES	Complex Exponential Smoothing	TBA	Yes
SSARIMA	State Space ARIMA	TBA	Yes
MSARIMA	Multiple Seasonal ARIMA	TBA	Yes
GUM	Generalised Univariate Model	TBA	Yes
SMA	Simple Moving Average	TBA	Yes
OES	Occurrence ETS for intermittent demand	TBA	Yes

Utility Functions

Function	Description	Python	R
msdecompose	Multiple seasonal decomposition (used for ADAM/ES initialization)	Yes	Yes
lowess	Scatter plot smoothing from Cleveland, W. S. (1979).	Yes	in stats package

lowess was implemented in Python to fully reproduce R's behaviour. The other existing Python implementations were not as accurate.

Getting Started

Python

from smooth import ADAM, ES, msdecompose

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

# 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)

Recommended Function

ADAM is the recommended function for most forecasting tasks. It provides:

• Unified ETS and ARIMA framework
• Multiple seasonality support
• Various error distributions
• Intermittent demand handling
• External regressors
• Automatic model selection
• ... and more

Common Parameters

These pages document parameters shared across multiple functions:

• Model-Specification - The model parameter, ETS taxonomy, and model type methods
• Orders-and-Lags - ARIMA orders and seasonal lags
• Loss-Functions - Loss functions for estimation (MSE, MAE, likelihood, etc.)
• Explanatory-Variables - External regressors via formula and xreg
• Initialisation - The initial parameter and state initialization
• Persistence - Smoothing parameters (alpha, beta, gamma) and phi
• Bounds - Parameter bounds and stability restrictions

Methods and Tools

Output and Visualisation

• Visualisation-and-Output - plot(), print(), summary(), xtable()

Parameters and Forecasts

• Coefficients-and-Parameters - coef(), confint(), vcov(), coefbootstrap()
• Fitted-Values-and-Forecasts - fitted(), actuals(), predict(), forecast()

Residuals and Diagnostics

• Residuals-and-Errors - residuals(), rstandard(), rmultistep(), outlierdummy()

Model Comparison

• Likelihood-and-Information-Criteria - logLik(), AIC(), BIC(), accuracy(), pls()

Model Information

• Model-Information - nobs(), nparam(), sigma(), extractScale()

Advanced Methods

• Simulation-Functions - simulate(), sim.es(), sim.ssarima(), sim.ces(), sim.gum(), sim.sma()
• Refitting-and-Reforecasting - reapply(), reforecast()
• Scale-Model - sm() for modelling heteroscedasticity

Additional Resources

• Resources - Publications and DOIs for each function