Exponential smoothing state space model

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,
  biasadj = FALSE,
  lower = c(rep(1e-04, 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,
  na.action = c("na.contiguous", "na.interp", "na.fail"),
  ...
)

Arguments

y

a numeric vector or time series of class ts

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 "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 y without re-estimating any smoothing parameters. See also the use.initial.values argument.

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. If lambda="auto", then a transformation is automatically selected using BoxCox.lambda. The transformation is ignored if NULL. Otherwise, data transformed before model is estimated. When lambda is specified, additive.only is set to TRUE.

biasadj

Use adjusted back-transformed mean for Box-Cox transformations. If transformed data is used to produce forecasts and fitted values, a regular back transformation will result in median forecasts. If biasadj is TRUE, an adjustment will be made to produce mean forecasts and fitted values.

lower

Lower bounds for the parameters (alpha, beta, gamma, phi). Ignored if bounds=="admissible".

upper

Upper bounds for the parameters (alpha, beta, gamma, phi). Ignored if bounds=="admissible".

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<=30).

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 intersection of these regions.

ic

Information criterion to be used in model selection.

restrict

If TRUE (default), the models with infinite variance will not be allowed.

allow.multiplicative.trend

If 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 model="MMN").

use.initial.values

If TRUE and model is of class "ets", then the initial values in the model are also not re-estimated.

na.action

A function which indicates what should happen when the data contains NA values. By default, the largest contiguous portion of the time-series will be used.

...

Other undocumented arguments.

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.

Author

Rob J Hyndman

Examples

fit <- ets(USAccDeaths)
plot(forecast(fit))