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Ivan Svetunkov edited this page May 15, 2026 · 3 revisions

AID — Automatic Identification of Demand

Overview

AID (Automatic Identification of Demand) classifies a univariate time series of demand observations into one of six demand categories and flags three kinds of anomalies (stockouts, new products, obsolete products). The procedure is model-based: it fits a small set of candidate ALM models to the cleaned series and picks the type whose model has the lowest information criterion.

Two entry points are provided in both implementations:

  • aid() — Run AID on a single time series.
  • R aidCat() / Python aid_cat() — Apply AID to a collection of series (matrix columns, data frame, or dict) and return a 2×3 category table plus anomaly counts.

The procedure is described in Svetunkov & Sroginis (2025); see References.

Algorithm

  1. Stockout detection — Build the vector of inter-demand intervals (gaps between non-zero observations). Smooth it with LOWESS. Fit a Geometric ALM (distribution="dgeom"). Compute the cumulative likelihood at each interval; values above the confidence level are flagged as stockouts. Leading and trailing zero runs are interpreted as a new product and an obsolete product respectively; the geometric model is refit on the trimmed data when either flag is set.

  2. Demand-type classification — Drop the stockout periods and the leading/trailing zero runs. Build a smoothed regressor via SuperSmoother. Fit up to four candidate ALMs:

    Slot Distribution Mixture Demand category
    1 drectnorm — smooth intermittent fractional
    2 dnorm + Bernoulli occurrence lumpy intermittent fractional
    3 dnbinom — smooth intermittent count
    4 dnbinom + Bernoulli occurrence lumpy intermittent count

    When the cleaned series contains no zeros, only two regular candidates (dnorm, dnbinom) are considered. Special branches handle binary data and very-low-volume data. The candidate with the smallest information criterion gives the final classification.

Demand categories

Type 1 Type 2 Type 2a Name
count regular — regular count
fractional regular — regular fractional
count intermittent smooth smooth intermittent count
fractional intermittent smooth smooth intermittent fractional
count intermittent lumpy lumpy intermittent count
fractional intermittent lumpy lumpy intermittent fractional

aid() — single series

Parameters

Parameter R Python Type Default Description
series y y numeric vector / array_like — Time series (NA/NaN values are replaced by 0).
ic ic ic character / str "AICc" Information criterion: "AIC", "AICc", "BIC", "BICc".
level level level numeric / float 0.99 Confidence level for the stockout detection.
loss loss loss character / str "likelihood" Loss function passed to alm() / ALM().
extras ... **alm_kwargs — — Additional arguments forwarded to alm() / ALM().

Return Value

R returns an S3 object of class "aid"; Python returns an AidResult. Both expose the same fields:

Field Description
y Original series (NAs replaced by 0).
models Named list / dict of fitted candidate models, plus the stockout model when applicable.
name Selected demand type (one of the six category names).
type Sub-categorisation with elements type1, type2, type2a.
stockouts Sub-list / dict with start, end (1-based positions in the original series), dummy, new, obsolete (binary indicator vectors of length n).
new TRUE/True if leading zeros indicate a new product.
obsolete TRUE/True if trailing zeros indicate a discontinued product.

Examples

Intermittent count demand

# R
set.seed(42)
y <- rpois(120, 0.7)
res <- aid(y)
print(res)
# Python
import numpy as np
from greybox import aid

rng = np.random.default_rng(42)
y = rng.poisson(0.7, 120).astype(float)
res = aid(y)
print(res)
# The provided time series is smooth intermittent count

Injected stockout

# R
set.seed(0)
y <- rpois(100, 3); y[41:50] <- 0
res <- aid(y)
res$stockouts$start  # 41
res$stockouts$end    # 50
# Python
rng = np.random.default_rng(0)
y = rng.poisson(3, 100).astype(float)
y[40:50] = 0  # 0-based slice = 1-based 41..50
res = aid(y)
res.stockouts["start"]  # array([41])  -- 1-based, matches R
res.stockouts["end"]    # array([50])

New product (leading zeros)

# R
y <- c(rep(0, 20), rpois(80, 5))
res <- aid(y)
res$new       # TRUE
# Python
y = np.concatenate([np.zeros(20), rng.poisson(5, 80)])
res = aid(y)
res.new        # True

aidCat() / aid_cat() — multiple series

Parameters

Parameter R Python Type Default Description
data data data matrix / data.frame / array_like or DataFrame or dict — Columns / entries are treated as individual series.
extras ... **aid_kwargs — — Forwarded to aid() (e.g. ic="BIC", level=0.95).

Return Value

R returns an object of class "aidCat"; Python returns an AidCatResult. Both contain:

Field R Python
categories factor vector of demand types pandas.Categorical
types 2×3 frequency matrix pandas.DataFrame indexed by ["Count","Fractional"] × ["Regular","Smooth Intermittent","Lumpy Intermittent"]
anomalies named vector New / Stockouts / Old pandas.Series with the same index
(extra) — results — list of per-series AidResult objects

Example — multi-series tabulation

# R
set.seed(1)
xreg <- cbind(
  x1 = rpois(80, 1),
  x2 = rpois(80, 5),
  x3 = rnorm(80, 10, 2)
)
cat <- aidCat(xreg)
print(cat)
# Python
import numpy as np
from greybox import aid_cat

rng = np.random.default_rng(1)
series = {
    "x1": rng.poisson(1, 80).astype(float),
    "x2": rng.poisson(5, 80).astype(float),
    "x3": rng.normal(10, 2, 80),
}
cat = aid_cat(series)
print(cat)
# Demand categories:
#             Regular  Smooth Intermittent  Lumpy Intermittent
# Count             1                    1                   0
# Fractional        1                    0                   0
#
# Anomalies:
# New          0
# Stockouts    0
# Old          0

Methods on the result objects

Both implementations expose the same two methods on the aid / aid_cat return values:

Method R Python Description
print print(res) print(res) Demand-type and anomaly summary.
plot plot(res) res.plot() For aid(): time series with red/green stockout boundary lines and grey shading; leading-zero block shaded blue when new, trailing-zero block shaded orange when obsolete. For aid_cat(): the 2×3 demand-category panel with cell counts and row / column marginals.

Both implementations also expose the same fields directly: in R via $ (res$stockouts$start), in Python via attribute access (res.stockouts.start). The Python nested fields are typed dataclasses (AidType, Stockouts) that also support dict-style subscripts (res.stockouts["start"]) for backward compatibility with code written against the earlier dict-based API.

# Python — attribute access matches R's $.$.$ pattern
res = aid(y)
res.stockouts.start    # numpy.ndarray of 1-based positions
res.stockouts.dummy    # length-n 0/1 indicator vector
res.type.type1         # "count" or "fractional"

# Dict-style subscripts also work
res.stockouts["start"]
res.type["type1"]

ax = res.plot()        # matplotlib Axes

Notes on the Python implementation

  • Top-level imports: from greybox import aid, aid_cat.
  • matplotlib>=3.5 is a hard dependency, so res.plot() always works.
  • Mirrors the R algorithm one-to-one; categorical decisions (name, type, new, obsolete, stockouts$start/$end) match R exactly on the same input.
  • Numerical IC values agree with R to about 1e-3 because Python uses nlopt while R uses nloptr; the two optimisers converge to nearly-but-not-quite-identical optima.
  • Stockout positions in stockouts.start / stockouts.end are reported as 1-based indices to match R; the dummy, new, and obsolete arrays are positional (binary) vectors of length n and behave identically in both languages.
  • The internal smoothing steps use LOWESS and SuperSmoother, which match R to machine precision.

References

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