Feed-forward neural networks with a single hidden layer and lagged inputs for forecasting univariate time series.
NNETAR(formula, n_nodes = NULL, n_networks = 20, scale_inputs = TRUE, ...)
formula | Model specification (see "Specials" section). |
---|---|
n_nodes | Number of nodes in the hidden layer. Default is half of the number of input nodes (including external regressors, if given) plus 1. |
n_networks | Number of networks to fit with different random starting weights. These are then averaged when producing forecasts. |
scale_inputs | If TRUE, inputs are scaled by subtracting the column means and dividing by their respective standard deviations. Scaling is applied after transformations. |
... | Other arguments passed to |
A model specification.
A feed-forward neural network is fitted with lagged values of the response as
inputs and a single hidden layer with size
nodes. The inputs are for
lags 1 to p
, and lags m
to mP
where
m
is the seasonal period specified.
If exogenous regressors are provided, its columns are also used as inputs.
Missing values are currently not supported by this model.
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 non-linear 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 non-linear functions.
The AR
special is used to specify auto-regressive components in each of the
nodes of the neural network.
AR(p = NULL, P = 1, period = NULL)
p | The order of the non-seasonal auto-regressive (AR) terms. If p = NULL , an optimal number of lags will be selected for a linear AR(p) model via AIC. For seasonal time series, this will be computed on the seasonally adjusted data (via STL decomposition). |
P | The order of the seasonal auto-regressive (SAR) terms. |
period | The periodic nature of the seasonality. This can be either a number indicating the number of observations in each seasonal period, or text to indicate the duration of the seasonal window (for example, annual seasonality would be "1 year"). |
Exogenous regressors can be included in an NNETAR model without explicitly using the xreg()
special. Common exogenous regressor specials as specified in common_xregs
can also be used. These regressors are handled using stats::model.frame()
, and so interactions and other functionality behaves similarly to stats::lm()
.
xreg(...)
... | Bare expressions for the exogenous regressors (such as log(x) ) |
#> # A mable: 1 x 1 #> nn #> <model> #> 1 <NNAR(1,1)>