ces: Complex Exponential Smoothing

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/ces.R

Description

Function estimates CES in state space form with information potential equal to errors and returns several variables.

Usage

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ces(y, seasonality = c("none", "simple", "partial", "full"),
  initial = c("backcasting", "optimal"), a = NULL, b = NULL,
  ic = c("AICc", "AIC", "BIC", "BICc"), loss = c("likelihood", "MSE",
  "MAE", "HAM", "MSEh", "TMSE", "GTMSE", "MSCE"), h = 10, holdout = FALSE,
  cumulative = FALSE, interval = c("none", "parametric", "likelihood",
  "semiparametric", "nonparametric"), level = 0.95,
  bounds = c("admissible", "none"), silent = c("all", "graph", "legend",
  "output", "none"), xreg = NULL, xregDo = c("use", "select"),
  initialX = NULL, ...)

Arguments

y

Vector or ts object, containing data needed to be forecasted.

seasonality

The type of seasonality used in CES. Can be: none - No seasonality; simple - Simple seasonality, using lagged CES (based on t-m observation, where m is the seasonality lag); partial - Partial seasonality with real seasonal components (equivalent to additive seasonality); full - Full seasonality with complex seasonal components (can do both multiplicative and additive seasonality, depending on the data). First letter can be used instead of full words. Any seasonal CES can only be constructed for time series vectors.

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.

a

First complex smoothing parameter. Should be a complex number.

NOTE! CES is very sensitive to a and b values so it is advised either to leave them alone, or to use values from previously estimated model.

b

Second complex smoothing parameter. Can be real if seasonality="partial". In case of seasonality="full" must be complex number.

ic

The information criterion used in the model selection procedure.

loss

The type of Loss Function used in optimization. loss can be: likelihood (assuming Normal distribution of error term), MSE (Mean Squared Error), MAE (Mean Absolute Error), HAM (Half Absolute Moment), TMSE - Trace Mean Squared Error, GTMSE - Geometric Trace Mean Squared Error, MSEh - optimisation using only h-steps ahead error, MSCE - Mean Squared Cumulative Error. If loss!="MSE", then likelihood and model selection is done based on equivalent MSE. Model selection in this cases becomes not optimal.

There are also available analytical approximations for multistep functions: aMSEh, aTMSE and aGTMSE. These can be useful in cases of small samples.

Finally, just for fun the absolute and half analogues of multistep estimators are available: MAEh, TMAE, GTMAE, MACE, TMAE, HAMh, THAM, GTHAM, CHAM.

h

Length of forecasting horizon.

holdout

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

cumulative

If TRUE, then the cumulative forecast and prediction interval are produced instead of the normal ones. This is useful for inventory control systems.

interval

Type of interval to construct. This can be:

  • "none", aka "n" - do not produce prediction interval.

  • "parametric", "p" - use state-space structure of ETS. In case of mixed models this is done using simulations, which may take longer time than for the pure additive and pure multiplicative models. This type of interval relies on unbiased estimate of in-sample error variance, which divides the sume of squared errors by T-k rather than just T.

  • "likelihood", "l" - these are the same as "p", but relies on the biased estimate of variance from the likelihood (division by T, not by T-k).

  • "semiparametric", "sp" - interval based on covariance matrix of 1 to h steps ahead errors and assumption of normal / log-normal distribution (depending on error type).

  • "nonparametric", "np" - interval based on values from a quantile regression on error matrix (see Taylor and Bunn, 1999). The model used in this process is e[j] = a j^b, where j=1,..,h.

The parameter also accepts TRUE and FALSE. The former means that parametric interval are constructed, while the latter is equivalent to none. If the forecasts of the models were combined, then the interval are combined quantile-wise (Lichtendahl et al., 2013).

level

Confidence level. Defines width of prediction interval.

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.

xregDo

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.

...

Other non-documented parameters. For example parameter model can accept a previously estimated CES model and use all its parameters. FI=TRUE will make the function produce Fisher Information matrix, which then can be used to calculated variances of parameters of the model.

Details

The function estimates Complex Exponential Smoothing in the state space 2 described in Svetunkov, Kourentzes (2017) with the information potential equal to the approximation error. The estimation of initial states of xt is done using backcast.

For some more information about the model and its implementation, see the vignette: vignette("ces","smooth")

Value

Object of class "smooth" is returned. It contains the list of the following values:

Author(s)

Ivan Svetunkov, ivan@svetunkov.ru

References

See Also

es, ts, auto.ces

Examples

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y <- rnorm(100,10,3)
ces(y,h=20,holdout=TRUE)
ces(y,h=20,holdout=FALSE)

y <- 500 - c(1:100)*0.5 + rnorm(100,10,3)
ces(y,h=20,holdout=TRUE,interval="p",bounds="a")

ces(Mcomp::M3[[740]],h=8,holdout=TRUE,seasonality="s",interval="sp",level=0.8)

ces(Mcomp::M3[[1683]],h=18,holdout=TRUE,seasonality="s",interval="sp")
ces(Mcomp::M3[[1683]],h=18,holdout=TRUE,seasonality="p",interval="np")
ces(Mcomp::M3[[1683]],h=18,holdout=TRUE,seasonality="f",interval="p")

x <- cbind(c(rep(0,25),1,rep(0,43)),c(rep(0,10),1,rep(0,58)))
ces(Mcomp::M3[[1457]],holdout=TRUE,interval="np",xreg=x,loss="TMSE")

config-i1/smooth documentation built on June 16, 2021, 2:13 p.m.