nnetar: Neural Network Time Series Forecasts

Description

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

Usage

nnetar(x, p, P=1, size, repeats=20, xreg=NULL, lambda=NULL, model=NULL, subset=NULL, scale.inputs=TRUE, ...)
"forecast"(object, h=ifelse(object$m > 1, 2 * object$m, 10), xreg=NULL, lambda=object$lambda, ...)

Arguments

A numeric vector or time series.

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.

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 x. 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 x 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 x. 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.

object

An object of class nnetar generated by nnetar.

Number of periods for forecasting.

...

Other arguments passed to nnet for nnetar but ignored for forecast.nnetar.

Value

model: A list containing information about the fitted model
method: The name of the forecasting method as a character string
mean: Point forecasts as a time series
x: The original time series (either object itself or the time series used to create the model stored as object).
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

Details

A feed-forward neural network is fitted with lagged values of x 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(x). If there are missing values in x 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.

Examples

Run this code

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)

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