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 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. If
lambda="auto", then a transformation is automatically selected usingBoxCox.lambda. The transformation is ignored if NULL. Otherwise, data transformed before model is estimated.- model
Output from a previous call to
nnetar. If model is passed, this same model is fitted toywithout 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
lambdais notNULL, scaling is applied after Box-Cox transformation.- x
Deprecated. Included for backwards compatibility.
- …
Other arguments passed to
nnetfornnetar.
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 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.
Value
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
Examples
# NOT RUN {
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)
# }