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

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"))
methodThe 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))
methodThe form of the trend term: either none ("N"), additive ("A"), multiplicative ("M") or damped variants ("Ad", "Md").
alphaThe 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_rangeIf alpha=NULL, alpha_range provides bounds for the optimised value of alpha.
betaThe 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_rangeIf beta=NULL, beta_range provides bounds for the optimised value of beta.
phiThe 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_rangeIf 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))
methodThe form of the seasonal term: either none ("N"), additive ("A") or multiplicative ("M").
periodThe 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").
gammaThe 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_rangeIf 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.

See also

Examples

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