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).

opt_crit

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).

nmse

If opt_crit == "amse", nmse provides the 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

The information criterion used in selecting the model.

restrict

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

...

Other arguments

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, alpharange = c(1e-04, 0.9999),
      beta = NULL, betarange = c(1e-04, 0.9999),
      phi = NULL, phirange = 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 = 1the level will update similarly to a random walk process.
alpharange
If
alpha=NULL,
alpharangeprovides 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 = 1the level will slope will have no memory of past slopes.
betarange
If
beta=NULL,
betarangeprovides 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 = 1the slope will not be dampened.
phirange
If
phi=NULL,
phirangeprovides 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, gammarange = 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 = 1the seasonality will have no memory of past seasonal periods.
gammarange
If
gamma=NULL,
gammarangeprovides 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.

See also

Examples

USAccDeaths %>% as_tsibble %>% model(ETS(log(value) ~ season("A")))
#> # A mable: 1 x 1 #> `ETS(log(value) ~ season("A"))` #> <model> #> 1 <ETS(A,A,A)>