| Arima {forecast} | R Documentation |
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 re-apply it to the data x.
Arima(x, order=c(0,0,0), seasonal=list(order=c(0,0,0), period=NA),
xreg=NULL, include.mean=TRUE, include.drift=FALSE,
include.constant, lambda=model$lambda, transform.pars=TRUE,
fixed=NULL, init=NULL, method=c("CSS-ML","ML","CSS"), n.cond,
optim.control=list(), kappa=1e6, model=NULL)
x |
a univariate time series |
order |
A specification of the non-seasonal 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(x)). 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 vector or matrix of external regressors, which must have the same number of rows as x. |
include.mean |
Should the ARIMA model include a mean term? The default is TRUE for undifferenced series, FALSE for differenced ones (where a mean would not affect the fit nor predictions). |
include.drift |
Should the ARIMA model include a linear drift term? (i.e., a linear regression with ARIMA errors is fitted.) The default is FALSE. |
include.constant |
If TRUE, then |
lambda |
Box-Cox transformation parameter. Ignored if NULL. Otherwise, data transformed before model is estimated. |
transform.pars |
Logical. If true, the AR parameters are transformed to ensure that they remain in the region of stationarity. Not used for method="CSS". |
fixed |
optional numeric vector of the same length as the total number of parameters. If supplied, only NA entries in fixed will be varied. transform.pars=TRUE will be overridden (with a warning) if any AR parameters are fixed. It may be wise to set transform.pars=FALSE when fixing MA parameters, especially near non-invertibility. |
init |
optional numeric vector of initial parameter values. Missing values will be filled in, by zeroes except for regression coefficients. Values already specified in fixed will be ignored. |
method |
Fitting method: maximum likelihood or minimize conditional sum-of-squares. The default (unless there are missing values) is to use conditional-sum-of-squares to find starting values, then maximum likelihood. |
n.cond |
Only used if fitting by conditional-sum-of-squares: the number of initial observations to ignore. It will be ignored if less than the maximum lag of an AR term. |
optim.control |
List of control parameters for optim. |
kappa |
the prior variance (as a multiple of the innovations variance) for the past observations in a differenced model. Do not reduce this. |
model |
Output from a previous call to |
See the arima function in the stats package.
See the arima function in the stats package. The additional objects returned are
x |
The time series data |
xreg |
The regressors used in fitting (when relevant). |
Rob J Hyndman
fit <- Arima(WWWusage,order=c(3,1,0))
plot(forecast(fit,h=20))
# 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.
# in-sample one-step forecasts.
accuracy(air.model)
# out-of-sample one-step forecasts.
accuracy(air.model2)
# out-of-sample multi-step forecasts
accuracy(forecast(air.model,h=48,lambda=NULL),
log(window(AirPassengers,start=1957)))