Exponential smoothing state space model
Returns ets model applied to
ets(y, model="ZZZ", damped=NULL, alpha=NULL, beta=NULL, gamma=NULL, phi=NULL, additive.only=FALSE, lambda=NULL, biasadj=FALSE, 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("aicc","aic","bic"), restrict=TRUE, allow.multiplicative.trend=FALSE, use.initial.values=FALSE, ...)
- a numeric vector or time series
- 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 "Z"); and the third letter denotes the season type ("N","A","M" or "Z").
In all cases, "N"=none, "A"=additive, "M"=multiplicative and "Z"=automatically selected.
So, for example, "ANN" is simple exponential smoothing with additive errors,
"MAM" is multiplicative Holt-Winters' method with multiplicative errors, and so on.
It is also possible for the model to be of class
"ets", and equal to the output from a previous call to
ets. In this case, the same model is fitted to
ywithout re-estimating any smoothing parameters. See also the
- 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
- Value of alpha. If NULL, it is estimated.
- Value of beta. If NULL, it is estimated.
- Value of gamma. If NULL, it is estimated.
- Value of phi. If NULL, it is estimated.
- If TRUE, will only consider additive models. Default is FALSE.
- Box-Cox transformation parameter. Ignored if NULL. Otherwise, data transformed before model is estimated. When
additive.onlyis set to FALSE.
- Use adjusted back-transformed mean for Box-Cox transformations. If TRUE, point forecasts and fitted values are mean forecast. Otherwise, these points can be considered the median of the forecast densities.
- Lower bounds for the parameters (alpha, beta, gamma, phi)
- Upper bounds for the parameters (alpha, beta, gamma, phi)
- Optimization criterion. One of "mse" (Mean Square Error),
"amse" (Average MSE over first
nmseforecast horizons), "sigma" (Standard deviation of residuals), "mae" (Mean of absolute residuals), or "lik" (Log-likelihood, the default).
- Number of steps for average multistep MSE (1<=
- 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 intersection of these regions.
- Information criterion to be used in model selection.
TRUE(default), the models with infinite variance will not be allowed.
TRUE, models with multiplicative trend are allowed when searching for a model. Otherwise, the model space excludes them. This argument is ignored if a multiplicative trend model is explicitly requested (e.g., using
modelis of class
"ets", then the initial values in the model are also not re-estimated.
- Other undocumented arguments.
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.)
ets".The generic accessor functions
residualsextract useful features of the value returned by
etsand associated functions.
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.