Returns ETS model specified by the formula.

ETS(formula, opt_crit = c("lik", "amse", "mse", "sigma", "mae"),
nmse = 3, bounds = c("both", "usual", "admissible"), ic = c("aicc",
"aic", "bic"), restrict = TRUE, ...)

## Arguments

formula Model specification (see "Specials" section). The optimization criterion. Defaults to the log-likelihood "lik", but can also be set to "mse" (Mean Square Error), "amse" (Average MSE over first nmse forecast horizons), "sigma" (Standard deviation of residuals), or "mae" (Mean Absolute Error). If opt_crit == "amse", nmse provides the number of steps for average multistep MSE (1<=nmse<=30). 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. The information criterion used in selecting the model. If TRUE (default), the models with infinite variance will not be allowed. Other arguments

## Value

A model specification.

## Details

Based on the classification of methods as described in Hyndman et al (2008).

The methodology is fully automatic. The model is chosen automatically if not specified. This methodology performed extremely well on the M3-competition data. (See Hyndman, et al, 2002, below.)

## Specials

### error

The error special is used to specify the form of the error term.

error(method = c("A", "M"))

 method The form of the error term: either additive ("A") or multiplicative ("M").

### trend

The trend special is used to specify the form of the trend term and associated parameters.

trend(method = c("N", "A", "Ad"),
alpha = NULL, alpha_range = c(1e-04, 0.9999),
beta = NULL, beta_range = c(1e-04, 0.9999),
phi = NULL, phi_range = c(0.8, 0.98))

 method The form of the trend term: either none ("N"), additive ("A"), multiplicative ("M") or damped variants ("Ad", "Md"). alpha The value of the smoothing parameter for the level. If alpha = 0, the level will not change over time. Conversely, if alpha = 1 the level will update similarly to a random walk process. alpha_range If alpha=NULL, alpha_range provides bounds for the optimised value of alpha. beta The value of the smoothing parameter for the slope. If beta = 0, the slope will not change over time. Conversely, if beta = 1 the slope will have no memory of past slopes. beta_range If beta=NULL, beta_range provides bounds for the optimised value of beta. phi The value of the dampening parameter for the slope. If phi = 0, the slope will be dampened immediately (no slope). Conversely, if phi = 1 the slope will not be dampened. phi_range If phi=NULL, phi_range provides bounds for the optimised value of phi.

### season

The season special is used to specify the form of the seasonal term and associated parameters.

season(method = c("N", "A", "M"), period = NULL,
gamma = NULL, gamma_range = c(1e-04, 0.9999))

 method The form of the seasonal term: either none ("N"), additive ("A") or multiplicative ("M"). period The periodic nature of the seasonality. This can be either a number indicating the number of observations in each seasonal period, or text to indicate the duration of the seasonal window (for example, annual seasonality would be "1 year"). gamma The value of the smoothing parameter for the seasonal pattern. If gamma = 0, the seasonal pattern will not change over time. Conversely, if gamma = 1 the seasonality will have no memory of past seasonal periods. gamma_range If gamma=NULL, gamma_range provides bounds for the optimised value of gamma.

## 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.

as_tsibble(USAccDeaths) %>%
#>   ETS(log(value) ~ season("A"))