oes {smooth}

Occurrence ETS model

Description

Function returns the occurrence part of iETS model with the specified probability update and model types.

Usage

oes(y, model = "MNN", persistence = NULL, initial = "o",
  initialSeason = NULL, phi = NULL, occurrence = c("fixed", "general",
  "odds-ratio", "inverse-odds-ratio", "direct", "auto", "none"),
  ic = c("AICc", "AIC", "BIC", "BICc"), h = 10, holdout = FALSE,
  bounds = c("usual", "admissible", "none"), silent = c("all", "graph",
  "legend", "output", "none"), xreg = NULL, regressors = c("use",
  "select"), initialX = NULL, ...)

Arguments

y

Either numeric vector or time series vector.

model

The type of ETS model used for the estimation. Normally this should be "MNN" or any other pure multiplicative or additive model. The model selection is available here (although it's not fast), so you can use, for example, "YYN" and "XXN" for selecting between the pure multiplicative and pure additive models respectively. Using mixed models is possible, but not recommended.

persistence

Persistence vector g, containing smoothing parameters. If NULL, then estimated.

initial

Can be either character or a vector of initial states. If it is character, then it can be "optimal", meaning that the initial states are optimised, or "backcasting", meaning that the initials are produced using backcasting procedure.

initialSeason

The vector of the initial seasonal components. If NULL, then it is estimated.

phi

The value of the dampening parameter. Used only for damped-trend models.

occurrence

The type of model used in probability estimation. Can be "none" - none, "fixed" - constant probability, "odds-ratio" - the Odds-ratio model with b=1 in Beta distribution, "inverse-odds-ratio" - the model with a=1 in Beta distribution, "direct" - the TSB-like (Teunter et al., 2011) probability update mechanism a+b=1, "auto" - the automatically selected type of occurrence model, "general" - the general Beta model with two parameters. This will call oesg() function with two similar ETS models and the same provided parameters (initials and smoothing).

ic

The information criteria to use in case of model selection.

h

The forecast horizon.

holdout

If TRUE, holdout sample of size h is taken from the end of the data.

bounds

What type of bounds to use in the model estimation. The first letter can be used instead of the whole word.

silent

If silent="none", then nothing is silent, everything is printed out and drawn. silent="all" means that nothing is produced or drawn (except for warnings). In case of silent="graph", no graph is produced. If silent="legend", then legend of the graph is skipped. And finally silent="output" means that nothing is printed out in the console, but the graph is produced. silent also accepts TRUE and FALSE. In this case silent=TRUE is equivalent to silent="all", while silent=FALSE is equivalent to silent="none". The parameter also accepts first letter of words ("n", "a", "g", "l", "o").

xreg

The vector (either numeric or time series) or the matrix (or data.frame) of exogenous variables that should be included in the model. If matrix included than columns should contain variables and rows - observations. Note that xreg should have number of observations equal either to in-sample or to the whole series. If the number of observations in xreg is equal to in-sample, then values for the holdout sample are produced using es function.

regressors

The variable defines what to do with the provided xreg: "use" means that all of the data should be used, while "select" means that a selection using ic should be done. "combine" will be available at some point in future...

initialX

The vector of initial parameters for exogenous variables. Ignored if xreg is NULL.

...

The parameters passed to the optimiser, such as maxeval, xtol_rel, algorithm and print_level. The description of these is printed out by nloptr.print.options() function from the nloptr package. The default values in the oes function are maxeval=500, xtol_rel=1E-8, algorithm="NLOPT_LN_NELDERMEAD" and print_level=0.

Details

The function estimates probability of demand occurrence, using the selected ETS state space models.

For the details about the model and its implementation, see the respective vignette: vignette("oes","smooth")

Value

The object of class "occurrence" is returned. It contains following list of values:

• model - the type of the estimated ETS model;

• timeElapsed - the time elapsed for the construction of the model;

• fitted - the fitted values for the probability;

• fittedModel - the fitted values of the underlying ETS model, where applicable (only for occurrence=c("o","i","d"));

• forecast - the forecast of the probability for h observations ahead;

• forecastModel - the forecast of the underlying ETS model, where applicable (only for occurrence=c("o","i","d"));

• lower - the lower bound of the interval if interval!="none";

• upper - the upper bound of the interval if interval!="none";

• lowerModel - the lower bound of the interval of the underlying ETS model if interval!="none";

• upperModel - the upper bound of the interval of the underlying ETS model if interval!="none";

• states - the values of the state vector;

• logLik - the log-likelihood value of the model;

• nParam - the number of parameters in the model (the matrix is returned);

• residuals - the residuals of the model;

• y - actual values of occurrence (zeros and ones).

• persistence - the vector of smoothing parameters;

• phi - the value of the damped trend parameter;

• initial - initial values of the state vector;

• initialSeason - the matrix of initials seasonal states;

• occurrence - the type of the occurrence model;

• updateX - boolean, defining, if the states of exogenous variables were estimated as well.

• initialX - initial values for parameters of exogenous variables.

• persistenceX - persistence vector g for exogenous variables.

• transitionX - transition matrix F for exogenous variables.

• accuracy - The error measures for the forecast (in case of holdout=TRUE).

• B - the vector of all the estimated parameters (in case of "odds-ratio", "inverse-odds-ratio" and "direct" models).

Author(s)

Ivan Svetunkov, [e-mail]

References

• Svetunkov Ivan and Boylan John E. (2017). Multiplicative State-Space Models for Intermittent Time Series. Working Paper of Department of Management Science, Lancaster University, 2017:4 , 1-43.

• Teunter R., Syntetos A., Babai Z. (2011). Intermittent demand: Linking forecasting to inventory obsolescence. European Journal of Operational Research, 214, 606-615.

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

• Syntetos, A., Boylan J. (2005) The accuracy of intermittent demand estimates. International Journal of Forecasting, 21(2), 303-314.

See Also

adam, oesg, es

Examples

y <- rpois(100,0.1)
oes(y, occurrence="auto")

oes(y, occurrence="f")