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forecast (version 3.07)

ets: Exponential smoothing state space model

Description

Returns ets model applied to y.

Usage

ets(y, model="ZZZ", damped=NULL, alpha=NULL, beta=NULL, gamma=NULL, 
    phi=NULL, additive.only=FALSE, lambda=NULL, 
    lower=c(rep(0.0001,3), 0.8), upper=c(rep(0.9999,3),0.98), 
    opt.crit=c("lik","amse","mse","sigma","mae"), nmse=3, 
    bounds=c("both","usual","admissible"), ic=c("aic","aicc","bic"),
    restrict=TRUE)

Arguments

y
a numeric vector or time series
model
Usually a three-character string identifying method using the framework terminology of Hyndman et al. (2002) and Hyndman et al. (2008). The first letter denotes the error type ("A", "M" or "Z"); the second letter denotes the trend type ("N","A","M" or
damped
If TRUE, use a damped trend (either additive or multiplicative). If NULL, both damped and non-damped trends will be tried and the best model (according to the information criterion ic) returned.
alpha
Value of alpha. If NULL, it is estimated.
beta
Value of beta. If NULL, it is estimated.
gamma
Value of gamma. If NULL, it is estimated.
phi
Value of phi. If NULL, it is estimated.
additive.only
If TRUE, will only consider additive models. Default is FALSE.
lambda
Box-Cox transformation parameter. Ignored if NULL. Otherwise, data transformed before model is estimated. When lambda=TRUE, additive.only is set to FALSE.
lower
Lower bounds for the parameters (alpha, beta, gamma, phi)
upper
Upper bounds for the parameters (alpha, beta, gamma, phi)
opt.crit
Optimization criterion. One of "mse" (Mean Square Error), "amse" (Average MSE over first nmse forecast horizons), "sigma" (Standard deviation of residuals), "mae" (Mean of absolute residuals), or "lik" (Log-likelihood, the default).
nmse
Number of steps for average multistep MSE (1<=nmse
bounds
Type of parameter space to impose: "usual" indicates all parameters must lie between specified lower and upper bounds; "admissible" indicates parameters must lie in the admissible space; "both" (default) takes the
ic
Information criterion to be used in model selection.
restrict
If TRUE, the models with infinite variance will not be allowed.

Value

  • An object of class "ets". The generic accessor functions fitted.values and residuals extract useful features of the value returned by ets and associated functions.

Details

Based on the classification of methods as described in Hyndman et al (2008). The methodology is fully automatic. The only required argument for ets is the time series. The model is chosen automatically if not specified. This methodology performed extremely well on the M3-competition data. (See Hyndman, et al, 2002, below.)

References

Hyndman, R.J., Koehler, A.B., Snyder, R.D., and Grose, S. (2002) "A state space framework for automatic forecasting using exponential smoothing methods", International J. Forecasting, 18(3), 439--454. Hyndman, R.J., Akram, Md., and Archibald, B. (2008) "The admissible parameter space for exponential smoothing models". Annals of Statistical Mathematics, 60(2), 407--426. Hyndman, R.J., Koehler, A.B., Ord, J.K., and Snyder, R.D. (2008) Forecasting with exponential smoothing: the state space approach, Springer-Verlag. http://www.exponentialsmoothing.net.

See Also

HoltWinters, rwf, arima.

Examples

Run this code
fit <- ets(USAccDeaths)
plot(forecast(fit))

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