Forecasts for intermittent demand using Croston's method

Returns forecasts and other information for Croston's forecasts applied to y.

Usage

# S3 method for class 'croston_model'
forecast(object, h = 10, ...)

croston(
  y,
  h = 10,
  alpha = 0.1,
  type = c("croston", "sba", "sbj"),
  x = y,
  opt_alpha = FALSE,
  opt_crit = c("mse", "mae"),
  init = c("naive", "mean")
)

Arguments

object: An object of class croston_model as returned by croston_model().
h: Number of periods for forecasting. Default value is twice the largest seasonal period (for seasonal data) or ten (for non-seasonal data).
...: Additional arguments affecting the forecasts produced. If model = NULL, forecast.ts passes these to ets() or stlf() depending on the frequency of the time series. If model is not NULL, the arguments are passed to the relevant modelling function.
y: a numeric vector or univariate time series of class ts
alpha: Smoothing parameter(s), each between 0 and 1. A single value (the default, 0.1) is shared by the demand and interval SES applications. A length-2 vector uses alpha[1] for the demand and alpha[2] for the interval.
type: Which variant of Croston's method to use. Defaults to "croston" for Croston's method, but can also be set to "sba" for the Syntetos-Boylan approximation, and "sbj" for the Shale-Boylan-Johnston method.
opt_alpha: If TRUE, optimize the smoothing parameter(s) starting from alpha. Defaults to FALSE, which uses alpha directly.
opt_crit: Optimization criterion when opt_alpha = TRUE. One of "mse" (mean squared error) or "mae" (mean absolute error).
init: Initial demand and interval values. Either a string method or a length-2 numeric c(demand, interval). The "naive" method (the default) takes the interval from the first interval and "mean" from the mean interval, both taking demand from the first non-zero value. String values are optimized alongside alpha when opt_alpha = TRUE, while numeric values are held fixed.
x: Deprecated. Included for backwards compatibility.

Value

An object of class forecast.

Details

Based on Croston's (1972) method for intermittent demand forecasting, also described in Shenstone and Hyndman (2005). Croston's method involves using simple exponential smoothing (SES) on the non-zero elements of the time series and a separate application of SES to the times between non-zero elements of the time series. The smoothing parameters of the two applications of SES are denoted by alpha, and may be shared (the default) or specified separately for the demand and interval components.

Note that prediction intervals are not computed as Croston's method has no underlying stochastic model.

forecast class

An object of class forecast is a list usually containing at least the following elements:

model: A list containing information about the fitted model
method: The name of the forecasting method as a character string
mean: Point forecasts as a time series
lower: Lower limits for prediction intervals
upper: Upper limits for prediction intervals
level: The confidence values associated with the prediction intervals
x: The original time series.
residuals: Residuals from the fitted model. For models with additive errors, the residuals will be x minus the fitted values.
fitted: Fitted values (one-step forecasts)

The function summary can be used to obtain and print a summary of the results, while the functions plot and autoplot produce plots of the forecasts and prediction intervals. The generic accessor functions fitted.values and residuals extract various useful features from the underlying model.

References

Croston, J. (1972) "Forecasting and stock control for intermittent demands", Operational Research Quarterly, 23(3), 289-303.

Shale, E.A., Boylan, J.E., & Johnston, F.R. (2006). Forecasting for intermittent demand: the estimation of an unbiased average. Journal of the Operational Research Society, 57(5), 588-592.

Shenstone, L., and Hyndman, R.J. (2005) "Stochastic models underlying Croston's method for intermittent demand forecasting". Journal of Forecasting, 24, 389-402.

Syntetos A.A., Boylan J.E. (2001). On the bias of intermittent demand estimates. International Journal of Production Economics, 71, 457–466.

Author

Rob J Hyndman

Examples

y <- rpois(20, lambda = 0.3)
fcast <- croston(y)
autoplot(fcast)