Largely a wrapper for the arima
function in the stats
package. The main difference is that this function allows a drift term. It
is also possible to take an ARIMA model from a previous call to Arima
and reapply it to the data y
.
Arima( y, order = c(0, 0, 0), seasonal = c(0, 0, 0), xreg = NULL, include.mean = TRUE, include.drift = FALSE, include.constant, lambda = model$lambda, biasadj = FALSE, method = c("CSSML", "ML", "CSS"), model = NULL, x = y, ... )
y  a univariate time series of class 

order  A specification of the nonseasonal part of the ARIMA model: the three components (p, d, q) are the AR order, the degree of differencing, and the MA order. 
seasonal  A specification of the seasonal part of the ARIMA model, plus the period (which defaults to frequency(y)). This should be a list with components order and period, but a specification of just a numeric vector of length 3 will be turned into a suitable list with the specification as the order. 
xreg  Optionally, a numerical vector or matrix of external regressors, which must have the same number of rows as y. It should not be a data frame. 
include.mean  Should the ARIMA model include a mean term? The default
is 
include.drift  Should the ARIMA model include a linear drift term?
(i.e., a linear regression with ARIMA errors is fitted.) The default is

include.constant  If 
lambda  BoxCox transformation parameter. If 
biasadj  Use adjusted backtransformed mean for BoxCox transformations. If transformed data is used to produce forecasts and fitted values, a regular back transformation will result in median forecasts. If biasadj is TRUE, an adjustment will be made to produce mean forecasts and fitted values. 
method  Fitting method: maximum likelihood or minimize conditional sumofsquares. The default (unless there are missing values) is to use conditionalsumofsquares to find starting values, then maximum likelihood. 
model  Output from a previous call to 
x  Deprecated. Included for backwards compatibility. 
...  Additional arguments to be passed to 
See the arima
function in the stats package.
The additional objects returned are
The time series data
The regressors used in fitting (when relevant).
The bias adjusted MLE of the innovations variance.
See the arima
function in the stats package.
Rob J Hyndman
# Fit model to first few years of AirPassengers data air.model < Arima(window(AirPassengers,end=1956+11/12),order=c(0,1,1), seasonal=list(order=c(0,1,1),period=12),lambda=0) plot(forecast(air.model,h=48))lines(AirPassengers)# Apply fitted model to later data air.model2 < Arima(window(AirPassengers,start=1957),model=air.model) # Forecast accuracy measures on the log scale. # insample onestep forecasts. accuracy(air.model)#> ME RMSE MAE MPE MAPE MASE ACF1 #> Training set 0.3576253 7.89734 5.788344 0.1458472 2.670181 0.1982148 0.05807465#> ME RMSE MAE MPE MAPE MASE #> Training set 0.5159268 12.13132 8.14054 0.07949083 1.900931 0.2266508 #> ACF1 #> Training set 0.2166661# outofsample multistep forecasts accuracy(forecast(air.model,h=48,lambda=NULL), log(window(AirPassengers,start=1957)))#> ME RMSE MAE MPE MAPE MASE #> Training set 0.35762533 7.8973404 5.78834425 0.1458472 2.670181 0.1982148 #> Test set 0.08403416 0.1031891 0.08801596 1.3982000 1.463555 0.0030140 #> ACF1 Theil's U #> Training set 0.05807465 NA #> Test set 0.75730561 0.9290965