NNS.ARMA {NNS}

NNS ARMA

Description

Autoregressive model incorporating nonlinear regressions of component series.

Usage

NNS.ARMA(
  variable,
  h = 1,
  training.set = NULL,
  seasonal.factor = TRUE,
  weights = NULL,
  best.periods = 1,
  modulo = NULL,
  mod.only = TRUE,
  negative.values = FALSE,
  method = "nonlin",
  dynamic = FALSE,
  shrink = FALSE,
  plot = TRUE,
  seasonal.plot = TRUE,
  pred.int = NULL
)

Arguments

variable

a numeric vector.

h

integer; 1 (default) Number of periods to forecast.

training.set

numeric; NULL (default) Sets the number of variable observations

(variable[1 : training.set]) to monitor performance of forecast over in-sample range.

seasonal.factor

logical or integer(s); TRUE (default) Automatically selects the best seasonal lag from the seasonality test. To use weighted average of all seasonal lags set to (seasonal.factor = FALSE). Otherwise, directly input known frequency integer lag to use, i.e. (seasonal.factor = 12) for monthly data. Multiple frequency integers can also be used, i.e. (seasonal.factor = c(12, 24, 36))

weights

numeric or "equal"; NULL (default) sets the weights of the seasonal.factor vector when specified as integers. If (weights = NULL) each seasonal.factor is weighted on its NNS.seas result and number of observations it contains, else an "equal" weight is used.

best.periods

integer; [2] (default) used in conjunction with (seasonal.factor = FALSE), uses the best.periods number of detected seasonal lags instead of ALL lags when (seasonal.factor = FALSE, best.periods = NULL).

modulo

integer(s); NULL (default) Used to find the nearest multiple(s) in the reported seasonal period.

mod.only

logical; TRUE (default) Limits the number of seasonal periods returned to the specified modulo.

negative.values

logical; FALSE (default) If the variable can be negative, set to (negative.values = TRUE). If there are negative values within the variable, negative.values will automatically be detected.

method

options: ("lin", "nonlin", "both", "means"); "nonlin" (default) To select the regression type of the component series, select (method = "both") where both linear and nonlinear estimates are generated. To use a nonlinear regression, set to (method = "nonlin"); to use a linear regression set to (method = "lin"). Means for each subset are returned with (method = "means").

dynamic

logical; FALSE (default) To update the seasonal factor with each forecast point, set to (dynamic = TRUE). The default is (dynamic = FALSE) to retain the original seasonal factor from the inputted variable for all ensuing h.

shrink

logical; FALSE (default) Ensembles forecasts with method = "means".

plot

logical; TRUE (default) Returns the plot of all periods exhibiting seasonality and the variable level reference in upper panel. Lower panel returns original data and forecast.

seasonal.plot

logical; TRUE (default) Adds the seasonality plot above the forecast. Will be set to FALSE if no seasonality is detected or seasonal.factor is set to an integer value.

pred.int

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

Value

Returns a vector of forecasts of length (h) if no pred.int specified. Else, returns a data.table with the forecasts as well as lower and upper prediction intervals per forecast point.

Note

For monthly data series, increased accuracy may be realized from forcing seasonal factors to multiples of 12. For example, if the best periods reported are: {37, 47, 71, 73} use (seasonal.factor = c(36, 48, 72)).

(seasonal.factor = FALSE) can be a very computationally expensive exercise due to the number of seasonal periods detected.

Author(s)

Fred Viole, OVVO Financial Systems

References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp

Viole, F. (2019) "Forecasting Using NNS" https://www.ssrn.com/abstract=3382300

Examples

## Nonlinear NNS.ARMA using AirPassengers monthly data and 12 period lag
## Not run: 
NNS.ARMA(AirPassengers, h = 45, training.set = 100, seasonal.factor = 12, method = "nonlin")

## Linear NNS.ARMA using AirPassengers monthly data and 12, 24, and 36 period lags
NNS.ARMA(AirPassengers, h = 45, training.set = 120, seasonal.factor = c(12, 24, 36), method = "lin")

## Nonlinear NNS.ARMA using AirPassengers monthly data and 2 best periods lag
NNS.ARMA(AirPassengers, h = 45, training.set = 120, seasonal.factor = FALSE, best.periods = 2)

## End(Not run)