Feed-forward neural networks with a single hidden layer and lagged inputs for forecasting univariate time series.
nnetar( y, p, P = 1, size, repeats = 20, xreg = NULL, lambda = NULL, model = NULL, subset = NULL, scale.inputs = TRUE, x = y, ... )
A numeric vector or time series of class
Embedding dimension for non-seasonal time series. Number of non-seasonal lags used as inputs. For non-seasonal time series, the default is the optimal number of lags (according to the AIC) for a linear AR(p) model. For seasonal time series, the same method is used but applied to seasonally adjusted data (from an stl decomposition).
Number of seasonal lags used as inputs.
Number of nodes in the hidden layer. Default is half of the number of input nodes (including external regressors, if given) plus 1.
Number of networks to fit with different random starting weights. These are then averaged when producing forecasts.
Optionally, a vector or matrix of external regressors, which
must have the same number of rows as
Box-Cox transformation parameter. If
Output from a previous call to
Optional vector specifying a subset of observations to be used
in the fit. Can be an integer index vector or a logical vector the same
If TRUE, inputs are scaled by subtracting the column
means and dividing by their respective standard deviations. If
Deprecated. Included for backwards compatibility.
Other arguments passed to
Returns an object of class "
summary is used to obtain and print a summary of the
The generic accessor functions
extract useful features of the value returned by
A list containing information about the fitted model
The name of the forecasting method as a character string
The original time series.
The external regressors used in fitting (if given).
Residuals from the fitted model. That is x minus fitted values.
Fitted values (one-step forecasts)
A feed-forward neural network is fitted with lagged values of
inputs and a single hidden layer with
size nodes. The inputs are for
lags 1 to
p, and lags
xreg is provided, its columns are also
used as inputs. If there are missing values in
xreg, the corresponding rows (and any others which depend on them as
lags) are omitted from the fit. A total of
repeats networks are
fitted, each with random starting weights. These are then averaged when
computing forecasts. The network is trained for one-step forecasting.
Multi-step forecasts are computed recursively.
For non-seasonal data, the fitted model is denoted as an NNAR(p,k) model, where k is the number of hidden nodes. This is analogous to an AR(p) model but with nonlinear functions. For seasonal data, the fitted model is called an NNAR(p,P,k)[m] model, which is analogous to an ARIMA(p,0,0)(P,0,0)[m] model but with nonlinear functions.
Rob J Hyndman and Gabriel Caceres