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, ... )

y | A numeric vector or time series of class |
---|---|

p | 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). |

P | Number of seasonal lags used as inputs. |

size | Number of nodes in the hidden layer. Default is half of the number of input nodes (including external regressors, if given) plus 1. |

repeats | Number of networks to fit with different random starting weights. These are then averaged when producing forecasts. |

xreg | Optionally, a vector or matrix of external regressors, which
must have the same number of rows as |

lambda | Box-Cox transformation parameter. If |

model | Output from a previous call to |

subset | 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
length as |

scale.inputs | If TRUE, inputs are scaled by subtracting the column
means and dividing by their respective standard deviations. If |

x | Deprecated. Included for backwards compatibility. |

... | Other arguments passed to |

Returns an object of class "`nnetar`

".

The function `summary`

is used to obtain and print a summary of the
results.

The generic accessor functions `fitted.values`

and `residuals`

extract useful features of the value returned by `nnetar`

.

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)

Other arguments

A feed-forward neural network is fitted with lagged values of `y`

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=frequency(y)`

. If `xreg`

is provided, its columns are also
used as inputs. If there are missing values in `y`

or
`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

## Fit model to first 100 years of lynx data fit <- nnetar(window(lynx,end=1920), decay=0.5, maxit=150) plot(forecast(fit,h=14))## Apply fitted model to later data, including all optional arguments fit2 <- nnetar(window(lynx,start=1921), model=fit)