NNS ARMA Optimizer

Wrapper function for optimizing any combination of a given seasonal.factor vector in NNS.ARMA. Minimum sum of squared errors (forecast-actual) is used to determine optimum across all NNS.ARMA methods.

Usage

NNS.ARMA.optim(
  variable,
  h = NULL,
  training.set = NULL,
  seasonal.factor,
  lin.only = FALSE,
  negative.values = FALSE,
  obj.fn = expression(mean((predicted - actual)^2)/(NNS::Co.LPM(1, predicted, actual,
    target_x = mean(predicted), target_y = mean(actual)) + NNS::Co.UPM(1, predicted,
    actual, target_x = mean(predicted), target_y = mean(actual)))),
  objective = "min",
  linear.approximation = TRUE,
  ncores = NULL,
  pred.int = 0.95,
  print.trace = TRUE,
  plot = FALSE
)

Arguments

variable

a numeric vector.

h

integer; NULL (default) Number of periods to forecast out of sample. If NULL, h = length(variable) - training.set.

training.set

integer; NULL (default) Sets the number of variable observations as the training set. See Note below for recommended uses.

seasonal.factor

integers; Multiple frequency integers considered for NNS.ARMA model, i.e. (seasonal.factor = c(12, 24, 36)).

lin.only

logical; FALSE (default) For fast optimization of the linear regression method. More robust than lin.only = TRUE.

negative.values

logical; FALSE (default) If the variable can be negative, set to (negative.values = TRUE). It will automatically select (negative.values = TRUE) if the minimum value of the variable is negative.

obj.fn

expression; expression(cor(predicted, actual, method = "spearman") / sum((predicted - actual)^2)) (default) Rank correlation / sum of squared errors is the default objective function. Any expression(...) using the specific terms predicted and actual can be used.

objective

options: ("min", "max") "max" (default) Select whether to minimize or maximize the objective function obj.fn.

linear.approximation

logical; TRUE (default) Uses the best linear output from NNS.reg to generate a nonlinear and mixture regression for comparison. FALSE is a more exhaustive search over the objective space.

ncores

integer; value specifying the number of cores to be used in the parallelized procedure. If NULL (default), the number of cores to be used is equal to the number of cores of the machine - 1.

pred.int

numeric [0, 1]; 0.95 (default) Returns the associated prediction intervals for the final estimate. Constructed using the maximum entropy bootstrap NNS.meboot on the final estimates.

print.trace

logical; TRUE (default) Prints current iteration information. Suggested as backup in case of error, best parameters to that point still known and copyable!

plot

logical; FALSE (default)

Value

Returns a list containing:

• $period a vector of optimal seasonal periods

• $weights the optimal weights of each seasonal period between an equal weight or NULL weighting

• $obj.fn the objective function value

• $method the method identifying which NNS.ARMA method was used.

• $shrink whether to use the shrink parameter in NNS.ARMA.

• $nns.regress whether to smooth the variable via NNS.reg before forecasting.

• $bias.shift a numerical result of the overall bias of the optimum objective function result. To be added to the final result when using the NNS.ARMA with the derived parameters.

• $errors a vector of model errors from internal calibration.

• $results a vector of length h.

• $lower.pred.int a vector of lower prediction intervals per forecast point.

• $upper.pred.int a vector of upper prediction intervals per forecast point.

Note

• Typically, (training.set = 0.8 * length(variable)) is used for optimization. Smaller samples could use (training.set = 0.9 * length(variable)) (or larger) in order to preserve information.

• The number of combinations will grow prohibitively large, they should be kept as small as possible. seasonal.factor containing an element too large will result in an error. Please reduce the maximum seasonal.factor.

• Set (ncores = 1) if routine is used within a parallel architecture.

References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)

Author

Fred Viole, OVVO Financial Systems

Examples

## Nonlinear NNS.ARMA period optimization using 2 yearly lags on AirPassengers monthly data
if (FALSE) { # \dontrun{
nns.optims <- NNS.ARMA.optim(AirPassengers[1:132], training.set = 120,
seasonal.factor = seq(12, 24, 6))

## To predict out of sample using best parameters:
NNS.ARMA.optim(AirPassengers[1:132], h = 12, seasonal.factor = seq(12, 24, 6))

## Incorporate any objective function from external packages (such as \code{Metrics::mape})
NNS.ARMA.optim(AirPassengers[1:132], h = 12, seasonal.factor = seq(12, 24, 6),
obj.fn = expression(Metrics::mape(actual, predicted)), objective = "min")
} # }