Returns ets model applied to `y`

.

```
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"),
...
)
```

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.

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.

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.)

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`

.

# NOT RUN { fit <- ets(USAccDeaths) plot(forecast(fit)) # }