# Arima

From forecast v5.3
by Rob Hyndman

##### Fit ARIMA model to univariate time series

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`

.

- Keywords
- ts

##### Usage

```
Arima(x, order=c(0,0,0), seasonal=c(0,0,0),
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

- x
- 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.

##### Details

See the `arima`

function in the stats package.

##### Value

- 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).

##### See Also

##### Examples

```
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)))
```

*Documentation reproduced from package forecast, version 5.3, License: GPL (>= 2)*

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