# nnetar

##### Neural Network Time Series Forecasts

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

- Keywords
- ts

##### Usage

`nnetar(y, p, P=1, size, repeats=20, xreg=NULL, lambda=NULL, model=NULL, subset=NULL, scale.inputs=TRUE, x=y, ...)`

##### Arguments

- y
- A numeric vector or time series.
- 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`

.

##### Details

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 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.

##### Value

`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`

.##### Examples

```
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)
```

*Documentation reproduced from package forecast, version 7.3, License: GPL (>= 2)*