sim.gum {smooth}

Simulate Generalised Exponential Smoothing

Description

Function generates data using GUM with Single Source of Error as a data generating process.

Usage

sim.gum(orders = c(1), lags = c(1), obs = 10, nsim = 1,
  frequency = 1, measurement = NULL, transition = NULL,
  persistence = NULL, initial = NULL, randomizer = c("rnorm", "rt",
  "rlaplace", "rs"), probability = 1, ...)

Arguments

orders

Order of the model. Specified as vector of number of states with different lags. For example, orders=c(1,1) means that there are two states: one of the first lag type, the second of the second type.

lags

Defines lags for the corresponding orders. If, for example, orders=c(1,1) and lags are defined as lags=c(1,12), then the model will have two states: the first will have lag 1 and the second will have lag 12. The length of lags must correspond to the length of orders.

obs

Number of observations in each generated time series.

nsim

Number of series to generate (number of simulations to do).

frequency

Frequency of generated data. In cases of seasonal models must be greater than 1.

measurement

Measurement vector w. If NULL, then estimated.

transition

Transition matrix F. Can be provided as a vector. Matrix will be formed using the default matrix(transition,nc,nc), where nc is the number of components in state vector. If NULL, then estimated.

persistence

Persistence vector g, containing smoothing parameters. If NULL, then estimated.

initial

Vector of initial values for state matrix. If NULL, then generated using advanced, sophisticated technique - uniform distribution.

randomizer

Type of random number generator function used for error term. Defaults are: rnorm, rt, rlaplace and rs. rlnorm should be used for multiplicative models (e.g. ETS(M,N,N)). But any function from Distributions will do the trick if the appropriate parameters are passed. For example rpois with lambda=2 can be used as well, but might result in weird values.

probability

Probability of occurrence, used for intermittent data generation. This can be a vector, implying that probability varies in time (in TSB or Croston style).

...

Additional parameters passed to the chosen randomizer. All the parameters should be passed in the order they are used in chosen randomizer. For example, passing just sd=0.5 to rnorm function will lead to the call rnorm(obs, mean=0.5, sd=1).

Details

For the information about the function, see the vignette: vignette("simulate","smooth")

Value

List of the following values is returned:

• model - Name of GUM model.

• measurement - Matrix w.

• transition - Matrix F.

• persistence - Persistence vector. This is the place, where smoothing parameters live.

• initial - Initial values of GUM in a form of matrix. If nsim>1, then this is an array.

• data - Time series vector (or matrix if nsim>1) of the generated series.

• states - Matrix (or array if nsim>1) of states. States are in columns, time is in rows.

• residuals - Error terms used in the simulation. Either vector or matrix, depending on nsim.

• occurrence - Values of occurrence variable. Once again, can be either a vector or a matrix...

• logLik - Log-likelihood of the constructed model.

Author(s)

Ivan Svetunkov, [e-mail]

References

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

See Also

sim.es, sim.ssarima, sim.ces, gum, Distributions

Examples

# Create 120 observations from GUM(1[1]). Generate 100 time series of this kind.
x <- sim.gum(orders=c(1),lags=c(1),obs=120,nsim=100)

# Generate similar thing for seasonal series of GUM(1[1],1[4]])
x <- sim.gum(orders=c(1,1),lags=c(1,4),frequency=4,obs=80,nsim=100,transition=c(1,0,0.9,0.9))

# Estimate model and then generate 10 time series from it
ourModel <- gum(rnorm(100,100,5))
simulate(ourModel,nsim=10)