Arima: Fit ARIMA model to univariate time series

Description

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.

Usage

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)

Arguments

a univariate time series of class ts.

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

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 include.mean is set to be TRUE for undifferenced series and include.drift is set to be TRUE for differenced series. Note that if there is more than one difference taken, no constant is included regardless of the val

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.par

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 Arima. If model is passed, this same model is fitted to x without re-estimating any parameters.

Value

See the arima function in the stats package. The additional objects returned are
xThe time series data
xregThe regressors used in fitting (when relevant).

Details

See the arima function in the stats package.

Examples

Run this code

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)))