nnetar: Neural Network Time Series Forecasts
In a1967fa/f-cast: Forecasting Functions for Time Series and Linear Models

Description Usage Arguments Details Value Author(s) Examples

Feed-forward neural networks with a single hidden layer and lagged inputs for forecasting univariate time series.

1 2	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 `ts`.
`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 `y`. Must be numeric.
`lambda`	Box-Cox transformation parameter.
`model`	Output from a previous call to `nnetar`. If model is passed, this same model is fitted to `y` without re-estimating any parameters.
`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 `y`. All observations are used by default.
`scale.inputs`	If TRUE, inputs are scaled by subtracting the column means and dividing by their respective standard deviations. If `lambda` is not `NULL`, scaling is applied after Box-Cox transformation.
`x`	Deprecated. Included for backwards compatibility.
`...`	Other arguments passed to `nnet` for `nnetar`.

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.

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.

`model`	A list containing information about the fitted model
`method`	The name of the forecasting method as a character string
`x`	The original time series.
`xreg`	The external regressors used in fitting (if given).
`residuals`	Residuals from the fitted model. That is x minus fitted values.
`fitted`	Fitted values (one-step forecasts)
`...`	Other arguments

Rob J Hyndman and Gabriel Caceres

fit <- nnetar(lynx)
fcast <- forecast(fit)
plot(fcast)

## Arguments can be passed to nnet()
fit <- nnetar(lynx, decay=0.5, maxit=150)
plot(forecast(fit))
lines(lynx)

## 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))
lines(lynx)

## Apply fitted model to later data, including all optional arguments
fit2 <- nnetar(window(lynx,start=1921), model=fit)