Intermittent Demand¶

Croston variants for sparse/intermittent demand data from the IntermittentDemand module.

Overview¶

Intermittent demand data has many zero values with occasional non-zero "demands". Standard forecasting methods perform poorly on such data. The Croston family of methods decompose the problem into:

Demand size — the magnitude of non-zero demands
Inter-arrival time — the interval between non-zero demands

Three variants are provided:

Class	Method	Reference
`CrostonClassic`	Original Croston method	Croston (1972)
`CrostonSBA`	Syntetos-Boylan Approximation	Syntetos & Boylan (2001)
`CrostonSBJ`	Shale-Boylan-Johnston	Shale, Boylan & Johnston (2006)

CrostonClassic¶

from durbyn import CrostonClassic

data = [0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0,
        0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0]

model = CrostonClassic().fit(data)
fc = model.forecast(h=12)

print(fc.mean)            # flat forecast
print(model.fitted_values) # in-sample fitted values
print(model.residuals)     # in-sample residuals

CrostonSBA¶

from durbyn import CrostonSBA

model = CrostonSBA().fit(data)
fc = model.forecast(h=12)

CrostonSBJ¶

from durbyn import CrostonSBJ

model = CrostonSBJ().fit(data)
fc = model.forecast(h=12)

Shared Parameters¶

All three classes accept the same parameters:

Parameter	Type	Default	Description
`init_strategy`	`str`	`"mean"`	Initialisation: `"mean"` or `"naive"`
`number_of_params`	`int`	`2`	Number of smoothing parameters: `1` or `2`
`cost_metric`	`str`	`"mar"`	Cost metric: `"mar"`, `"msr"`, `"mae"`, `"mse"`
`optimize_init`	`bool`	`True`	Optimise initial values
`rm_missing`	`bool`	`False`	Remove missing values

Note

Intermittent demand models do not use a seasonal period m. They produce flat forecasts without prediction intervals.

Simple Croston¶

durbyn also provides a simpler Croston wrapper from the ExponentialSmoothing module:

from durbyn import Croston

model = Croston().fit(data)
fc = model.forecast(h=12)

See Exponential Smoothing for details.

Example: Comparing Variants¶

from durbyn import CrostonClassic, CrostonSBA, CrostonSBJ
import numpy as np

data = [6, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]

for cls in [CrostonClassic, CrostonSBA, CrostonSBJ]:
    model = cls().fit(data)
    fc = model.forecast(h=12)
    print(f"{cls.__name__}: forecast = {fc.mean[0]:.4f}")