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The greybox package is a toolbox for regression model building, selection and forecast evaluation. Its core is the Augmented Linear Model (ALM): a regression estimated by the likelihood of one of 25 distributions in R (26 in Python) or by another loss (8 named losses in R, 7 in Python, plus user-defined ones). Around it are stepwise selection, model combination, rolling-origin evaluation, error measures, measures of association, the identification of demand types, and data manipulation tools.

It is available for R (CRAN) and Python (PyPI). R is the original; the Python port has a scikit-learn-style interface and follows R's names, defaults and numbers.

Navigation aids

• Glossary — overloaded terms (distribution values vs d*() functions, loss vs ic, the meanings of lags, R $ vs Python .).
• Roadmap — what is R-only or not yet ported to Python.
• R-Python-differences — numerical-parity status and interface differences.
• Installation — installation instructions.
• Resources — academic references and DOIs.
• llms.txt — machine-readable index of every wiki page.

Quick Links

• CRAN Package
• PyPI Package
• GitHub Repository
• Statistics for Business Analytics (online book)

Functions

Models and selection

Page	R	Python	Description
ALM	alm()	ALM	Augmented Linear Model, with occurrence and scale parts and AR/I terms.
stepwise	stepwise()	stepwise()	Forward selection of regressors.
CALM	calm()	CALM()	Combination of ALMs weighted by information criteria.
distributions	d/p/q/r*()	d/p/q/r*()	Distribution families of ALM.

Evaluation

Page	R	Python	Description
measures	measures(), MAE(), MASE(), …	measures(), mae(), mase(), …	Point, interval, quantile and half-moment error measures.
rolling_origin	ro()	rolling_origin()	Rolling-origin evaluation.
RMCB	rmcb()	rmcb()	Nemenyi / MCB comparison of forecasting methods.

Analysis and diagnostics

Page	R	Python	Description
EDA	stick()	stick()	Seasonality / trend / irregular decomposition of the variance.
association	association(), pcor(), mcor(), cramer(), determination()	the same names	Measures of association.
diagnostics	outlierdummy()	outlier_dummy()	Outlier detection and dummies.
AID	aid(), aidCat()	aid(), aid_cat()	Automatic identification of demand.
Smoothers	lowess(), supsmu() (stats)	lowess(), supsmu()	LOWESS and SuperSmoother.

Data manipulation

Page	R	Python	Description
manipulations	xregExpander(), xregTransformer(), xregMultiplier(), temporaldummy(), B(), multipliers()	xreg_expander(), xreg_transformer(), xreg_multiplier(), temporal_dummy(), B(), multipliers()	Lags and leads, transformations, cross-products, calendar dummies, distributed lags.

Python also ships R's mtcars dataset as a pandas DataFrame: from greybox import mtcars.

Getting Started

R

install.packages("greybox")
library(greybox)

model <- alm(mpg ~ wt + hp, mtcars[1:28,], distribution="dnorm")
summary(model)

best <- stepwise(mtcars, ic="AICc")     # mpg ~ wt + qsec + am

forecasts <- predict(model, mtcars[29:32,])$mean
round(measures(mtcars$mpg[29:32], forecasts, mtcars$mpg[1:28]), 4)
#     ME    MAE    MSE    MPE   MAPE    sCE   sMAE   sMSE   MASE  RMSSE   SAME
# 0.3483 1.6205 4.3384 0.0349 0.0960 0.0683 0.0795 0.0104 0.4207 0.3734 0.0904
#   rMAE  rRMSE   rAME asymmetry   sPIS
# 0.1304 0.1639 0.0280    0.0530 -0.2036

y <- cumsum(rnorm(100))
ro(y, h=5, origins=10, call="list(mean=rep(mean(data), h))", value="mean")

Python

pip install greybox

import numpy as np
from greybox import ALM, formula, stepwise, measures, rolling_origin, mtcars

y, X = formula("mpg ~ wt + hp", mtcars.head(28))
model = ALM(distribution="dnorm").fit(X, y)
print(model.summary())

best = stepwise(mtcars, ic="AICc")      # mpg ~ 1 + wt + qsec + am

_, X_new = formula("mpg ~ wt + hp", mtcars.tail(4))
forecasts = model.predict(X_new).mean
measures(mtcars["mpg"].tail(4).to_numpy(), forecasts, y)
# {'ME': 0.3483, 'MAE': 1.6205, 'MSE': 4.3384, 'MPE': 0.0349, 'MAPE': 0.096, ...}   (rounded)

series = np.cumsum(np.random.default_rng(42).normal(size=100))
rolling_origin(series, h=5, origins=10, call=lambda data, h: np.full(h, data.mean()))

R ↔ Python parity matrix

"Yes" means implemented with the same defaults and results (see R-Python-differences); "R only" items are on Roadmap.

Area	R	Python	Status
Augmented Linear Model	alm()	ALM	Yes; dchisq Python only, QUALE loss R only
Scale model	sm(), implant()	sm(), implant(), ALM(scale_formula=)	Yes
Bootstrap of parameters	coefbootstrap(), vcov(bootstrap=TRUE)	coefbootstrap(), vcov(bootstrap=True)	Yes
Distributed lags	B(), multipliers()	B(), multipliers()	Yes
Stepwise selection	stepwise()	stepwise()	Yes
Model combination	calm()	CALM()	Partial (no formula, subset, parallel)
Dynamic combination	lmDynamic()	—	R only
Prediction	predict(), forecast()	predict()	Yes
Information criteria	AIC(), AICc(), BIC(), BICc()	aic, aicc, bic, bicc	Yes
Point likelihood	pointLik()	point_lik(), point_lik_cumulative()	Yes
Point information criteria	pAIC(), pAICc(), pBIC()	—	R only
Residual diagnostics	rstandard(), rstudent(), hatvalues(), cooks.distance()	rstandard(), rstudent(), hatvalues()	Partial (no Cook's distance)
Outlier dummies	outlierdummy()	outlier_dummy()	Yes
Distributions	d/p/q/r of the non-base families	d/p/q/r of all families	Yes, except dtplnorm (R only)
Error measures	measures(), ME(), MAE(), …, MIS(), pinball(), hm(), …	measures(), me(), mae(), …, mis(), pinball(), hm(), …	Yes; rmse() Python only
Accuracy of a model	accuracy()	—	R only
Rolling origin	ro()	rolling_origin()	Yes
RMCB	rmcb()	rmcb()	Yes
STI decomposition	stick()	stick()	Yes
Association	association(), pcor(), mcor(), cramer(), determination()	the same	Yes
Demand identification	aid(), aidCat()	aid(), aid_cat()	Yes
Smoothers	lowess(), supsmu() (stats)	lowess(), supsmu()	Yes
Regressor tools	xregExpander(), xregTransformer(), xregMultiplier(), temporaldummy()	xreg_expander(), xreg_transformer(), xreg_multiplier(), temporal_dummy()	Yes
Plots	graphmaker(), spread(), tableplot()	graphmaker(), spread(), tableplot()	Yes
Calendar and other utilities	detectdst(), detectleap(), polyprod(), dsrboot()	—	R only

Naming conventions

R uses camelCase or lower-case names; Python uses snake_case functions and PascalCase classes.

R	Python
alm()	ALM().fit()
calm()	CALM()
ro()	rolling_origin()
aidCat()	aid_cat()
pointLik()	point_lik()
outlierdummy()	outlier_dummy()
temporaldummy()	temporal_dummy()
xregExpander(), xregTransformer(), xregMultiplier()	xreg_expander(), xreg_transformer(), xreg_multiplier()
extractScale(), extractSigma()	extract_scale(), extract_sigma()
ME(), MAE(), rMIS(), …	me(), mae(), rmis(), …
x$name	x.name