smooth (version 1.9.9)

pls: Prediction Likelihood Score

Description

Function estimates Prediction Likelihood Score of the holdout actuals based on the model.

Usage

pls(actuals, forecasts, Etype = c("A", "M"), sigma, trace = TRUE,
  iprob = 1, digits = 5, ...)

Arguments

actuals

Actual values from the holdout.

forecasts

Point forecasts for the holdout (conditional mean).

Etype

Type of the error. If Etype="A", then normal distribution is used, if Etype="M", then log-normal distribution is used.

sigma

Value of variance of the errors. In case of trace=TRUE, this needs to be a covariance matrix of trace errors.

trace

If TRUE, then it is assumed that we are provided with trace forecasts (multiple steps ahead), Trace Forecast Likelihood is used in this case.

iprob

Vector of probabilities of occurrences for the holdout (only needed for intermittent models).

digits

Number of digits for rounding.

...

Other parameters passed to mean function.

Value

A value of the log-likelihood.

Details

Prediction likelihood score (PLS) is based on either normal or log-normal distribution of errors with the provided parameters. It returns the log of probability that the data was "produced" by the estimated model.

References

• Snyder, R. D., Ord, J. K., Beaumont, A., 2012. Forecasting the intermittent demand for slow-moving inventories: A modelling approach. International Journal of Forecasting 28 (2), 485-496.

• Kolassa, S., 2016. Evaluating predictive count data distributions in retail sales forecasting. International Journal of Forecasting 32 (3), 788-803.

Examples

# Generate data, apply es() with the holdout parameter and calculate PLS
x <- rnorm(100,0,1)
ourModel <- es(x, h=10, holdout=TRUE)
sigma <- t(ourModel$errors) %*% (ourModel$errors) / length(ourModel$residuals)
Etype <- substr(model.type(ourModel),1,1)
pls(actuals=ourModel$holdout, forecasts=ourModel$forecast, Etype=Etype,
    sigma=sigma, trace=TRUE)

# Do the same with intermittent data. Trace is not available yet for
# intermittent state-space models
x <- rpois(100,0.4)
ourModel <- es(x, h=10, holdout=TRUE, intermittent='a')
Etype <- substr(model.type(ourModel),1,1)
iprob <- window(ourModel$iprob,start(ourModel$holdout))
pls(actuals=ourModel$holdout, forecasts=ourModel$forecast, Etype=Etype,
    sigma=ourModel$s2, trace=FALSE, iprob=iprob)