ETS state-space (error/trend/seasonal)

Formula: the additive-error innovations state space form

  y_t = l_{t-1} + b_{t-1} + s_{t-m} + e_t
  l_t = l_{t-1} + b_{t-1} + alpha e_t
  b_t = b_{t-1}           + beta  e_t
  s_t = s_{t-m}           + gamma e_t

i.e. y_t = w' x_{t-1} + e_t, x_t = F x_{t-1} + g e_t. Smoothing parameters are chosen on a deterministic 0.1-step grid minimising the one-step sum of squared errors, or may be fixed directly.

Usage

Etsmod(
  y,
  error = "A",
  trend = FALSE,
  season = 0,
  alpha = NULL,
  beta = NULL,
  gamma = NULL
)

Arguments

y

Series.

error

Error type; only "A" (additive) is implemented.

trend

Include the additive local trend b_t.

season

Seasonal period m; 0 or 1 means no seasonal component.

alpha, beta, gamma

Fixed smoothing parameters (bypass the grid).

Value

List with estimate, alpha, beta, gamma, sse, sigma2, aic, level, slope, forecast, n, method.

References

Hyndman, Koehler, Snyder & Grose (2002), International Journal of Forecasting 18(3):439-454, doi:10.1016/S0169-2070(01)00110-8.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Etsmod(V)
#> $estimate
#> [1] 7.888889
#> 
#> $alpha
#> [1] 0.9
#> 
#> $beta
#> [1] 0
#> 
#> $gamma
#> [1] 0
#> 
#> $sse
#> [1] 8.380097
#> 
#> $sigma2
#> [1] 1.047512
#> 
#> $aic
#> [1] 4.371344
#> 
#> $level
#> [1] 7.888889
#> 
#> $slope
#> [1] 0
#> 
#> $forecast
#> [1] 7.888889
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "ETS state-space (error/trend/seasonal)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"