smooth (version 4.3.0)

gum: Generalised Univariate Model

Description

Function constructs Generalised Univariate Model, estimating matrices F, w, vector g and initial parameters.

Usage

gum(y, orders = c(1, 1), lags = c(1, frequency(y)), type = c("additive",
  "multiplicative"), initial = c("backcasting", "optimal", "two-stage",
  "complete"), persistence = NULL, transition = NULL,
  measurement = rep(1, sum(orders)), loss = c("likelihood", "MSE", "MAE",
  "HAM", "MSEh", "TMSE", "GTMSE", "MSCE"), h = 0, holdout = FALSE,
  bounds = c("admissible", "none"), silent = TRUE, model = NULL,
  xreg = NULL, regressors = c("use", "select", "adapt", "integrate"),
  initialX = NULL, ...)
auto.gum(y, orders = 3, lags = frequency(y), type = c("additive",
  "multiplicative", "select"), initial = c("backcasting", "optimal",
  "two-stage", "complete"), ic = c("AICc", "AIC", "BIC", "BICc"),
  loss = c("likelihood", "MSE", "MAE", "HAM", "MSEh", "TMSE", "GTMSE",
  "MSCE"), h = 0, holdout = FALSE, bounds = c("admissible", "none"),
  silent = TRUE, xreg = NULL, regressors = c("use", "select", "adapt",
  "integrate"), ...)
gum_old(y, orders = c(1, 1), lags = c(1, frequency(y)),
  type = c("additive", "multiplicative"), persistence = NULL,
  transition = NULL, measurement = rep(1, sum(orders)),
  initial = c("optimal", "backcasting"), loss = c("likelihood", "MSE",
  "MAE", "HAM", "MSEh", "TMSE", "GTMSE", "MSCE"), h = 10, holdout = FALSE,
  bounds = c("restricted", "admissible", "none"), silent = c("all",
  "graph", "legend", "output", "none"), xreg = NULL, regressors = c("use",
  "select"), initialX = NULL, ...)
ges(...)

Value

Object of class "adam" is returned with similar elements to the adam function.

Details

The function estimates the Single Source of Error state space model of the following type:

$$y_{t} = w_t' v_{t-l} + \epsilon_{t}$$

$$v_{t} = F v_{t-l} + g_{t} \epsilon_{t}$$

where \(v_{t}\) is the state vector (defined using orders) and \(l\) is the vector of lags, \(w_t\) is the measurement vector (which includes fixed elements and explanatory variables), \(F\) is the transition matrix, \(g_t\) is the persistence vector (includes explanatory variables as well if provided), finally, \(\epsilon_{t}\) is the error term.

For some more information about the model and its implementation, see the vignette: vignette("gum","smooth")

References

• Svetunkov I. (2023) Smooth forecasting with the smooth package in R. arXiv:2301.01790. tools:::Rd_expr_doi("10.48550/arXiv.2301.01790").

• Svetunkov I. (2015 - Inf) "smooth" package for R - series of posts about the underlying models and how to use them: https://openforecast.org/category/r-en/smooth/.

• Svetunkov, I., 2023. Smooth Forecasting with the Smooth Package in R. arXiv. tools:::Rd_expr_doi("10.48550/arXiv.2301.01790")

• Snyder, R. D., 1985. Recursive Estimation of Dynamic Linear Models. Journal of the Royal Statistical Society, Series B (Methodological) 47 (2), 272-276.

• Hyndman, R.J., Koehler, A.B., Ord, J.K., and Snyder, R.D. (2008) Forecasting with exponential smoothing: the state space approach, Springer-Verlag. tools:::Rd_expr_doi("10.1007/978-3-540-71918-2").

See Also

adam, es, ces

gum, es, ces, sim.es, ssarima

Examples

gum(BJsales, h=8, holdout=TRUE)

ourModel <- gum(rnorm(118,100,3), orders=c(2,1), lags=c(1,4), h=18, holdout=TRUE)

# Redo previous model on a new data and produce prediction interval
gum(rnorm(118,100,3), model=ourModel, h=18)

# Produce something crazy with optimal initials (not recommended)
gum(rnorm(118,100,3), orders=c(1,1,1), lags=c(1,3,5), h=18, holdout=TRUE, initial="o")

# Simpler model estimated using trace forecast error loss function and its analytical analogue
gum(rnorm(118,100,3), orders=c(1), lags=c(1), h=18, holdout=TRUE, bounds="n", loss="TMSE")


x <- rnorm(50,100,3)

# The best GUM model for the data
ourModel <- auto.gum(x, orders=2, lags=4, h=18, holdout=TRUE)

summary(ourModel)