# ets: Exponential smoothing state space model In forecast: Forecasting Functions for Time Series and Linear Models

## Description

Returns ets model applied to `y`.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```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) `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`<=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.

## 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.)

## 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.

Rob J Hyndman

## 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.

`HoltWinters`, `rwf`, `Arima`.
 ```1 2``` ```fit <- ets(USAccDeaths) plot(forecast(fit)) ```