sma: Simple Moving Average

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/sma.R

Description

Function constructs state space simple moving average of predefined order

Usage

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sma(y, order = NULL, ic = c("AICc", "AIC", "BIC", "BICc"), h = 10,
  holdout = FALSE, cumulative = FALSE, interval = c("none", "parametric",
  "likelihood", "semiparametric", "nonparametric"), level = 0.95,
  silent = c("all", "graph", "legend", "output", "none"), ...)

Arguments

y

Vector or ts object, containing data needed to be forecasted.

order

Order of simple moving average. If NULL, then it is selected automatically using information criteria.

ic

The information criterion used in the model selection procedure.

h

Length of forecasting horizon.

holdout

If TRUE, holdout sample of size h is taken from the end of the data.

cumulative

If TRUE, then the cumulative forecast and prediction interval are produced instead of the normal ones. This is useful for inventory control systems.

interval

Type of interval to construct. This can be:

  • "none", aka "n" - do not produce prediction interval.

  • "parametric", "p" - use state-space structure of ETS. In case of mixed models this is done using simulations, which may take longer time than for the pure additive and pure multiplicative models. This type of interval relies on unbiased estimate of in-sample error variance, which divides the sume of squared errors by T-k rather than just T.

  • "likelihood", "l" - these are the same as "p", but relies on the biased estimate of variance from the likelihood (division by T, not by T-k).

  • "semiparametric", "sp" - interval based on covariance matrix of 1 to h steps ahead errors and assumption of normal / log-normal distribution (depending on error type).

  • "nonparametric", "np" - interval based on values from a quantile regression on error matrix (see Taylor and Bunn, 1999). The model used in this process is e[j] = a j^b, where j=1,..,h.

The parameter also accepts TRUE and FALSE. The former means that parametric interval are constructed, while the latter is equivalent to none. If the forecasts of the models were combined, then the interval are combined quantile-wise (Lichtendahl et al., 2013).

level

Confidence level. Defines width of prediction interval.

silent

If silent="none", then nothing is silent, everything is printed out and drawn. silent="all" means that nothing is produced or drawn (except for warnings). In case of silent="graph", no graph is produced. If silent="legend", then legend of the graph is skipped. And finally silent="output" means that nothing is printed out in the console, but the graph is produced. silent also accepts TRUE and FALSE. In this case silent=TRUE is equivalent to silent="all", while silent=FALSE is equivalent to silent="none". The parameter also accepts first letter of words ("n", "a", "g", "l", "o").

...

Other non-documented parameters. For example parameter model can accept a previously estimated SMA model and use its parameters.

Details

The function constructs AR model in the Single Source of Error state space form based on the idea that:

y_{t} = \frac{1}{n} ∑_{j=1}^n y_{t-j}

which is AR(n) process, that can be modelled using:

y_{t} = w' v_{t-1} + ε_{t}

v_{t} = F v_{t-1} + g ε_{t}

Where v_{t} is a state vector.

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

Value

Object of class "smooth" is returned. It contains the list of the following values:

Author(s)

Ivan Svetunkov, ivan@svetunkov.ru

References

See Also

filter, es, ssarima

Examples

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# SMA of specific order
ourModel <- sma(rnorm(118,100,3),order=12,h=18,holdout=TRUE,interval="p")

# SMA of arbitrary order
ourModel <- sma(rnorm(118,100,3),h=18,holdout=TRUE,interval="sp")

summary(ourModel)
forecast(ourModel)
plot(forecast(ourModel))

config-i1/smooth documentation built on June 16, 2021, 2:13 p.m.