sim.sma: Simulate Simple Moving Average In config-i1/smooth: Forecasting Using State Space Models

Description

Function generates data using SMA in a Single Source of Error state space model as a data generating process.

Usage

 ```1 2 3``` ```sim.sma(order = NULL, obs = 10, nsim = 1, frequency = 1, initial = NULL, randomizer = c("rnorm", "rt", "rlaplace", "rs"), probability = 1, ...) ```

Arguments

 `order` Order of the modelled series. If omitted, then a random order from 1 to 100 is selected. `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. `initial` Vector of initial states for the model. If `NULL`, values are generated. `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 SMA model.

• `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.

• `initial` - Vector (or matrix) of initial values.

• `probability` - vector of probabilities used in the simulation.

• `intermittent` - type of the intermittent model used.

• `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, ivan@svetunkov.ru

References

• 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. doi: 10.1007/978-3-540-71918-2.

`es, ts, Distributions`
 ```1 2``` ```# Create 40 observations of quarterly data using AAA model with errors from normal distribution sma10 <- sim.sma(order=10,frequency=4,obs=40,randomizer="rnorm",mean=0,sd=100) ```