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 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("CSS-ML", "ML", "CSS"),
  model = NULL,
  x = y,
  ...
)

Arguments

y	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(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 `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 value of this argument. This is deliberate as otherwise quadratic and higher order polynomial trends would be induced.
lambda	Box-Cox transformation parameter. If `lambda="auto"`, then a transformation is automatically selected using `BoxCox.lambda`. The transformation is ignored if NULL. Otherwise, data transformed before model is estimated.
biasadj	Use adjusted back-transformed mean for Box-Cox 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 sum-of-squares. The default (unless there are missing values) is to use conditional-sum-of-squares to find starting values, then maximum likelihood.
model	Output from a previous call to `Arima`. If model is passed, this same model is fitted to `y` without re-estimating any parameters.
x	Deprecated. Included for backwards compatibility.
...	Additional arguments to be passed to `arima`.

Value

See the arima function in the stats package. The additional objects returned are

The time series data

xreg

The regressors used in fitting (when relevant).

sigma2

The bias adjusted MLE of the innovations variance.

Details

See the arima function in the stats package.

Author

Rob J Hyndman

Examples

library(ggplot2)
WWWusage %>%
  Arima(order=c(3,1,0)) %>%
  forecast(h=20) %>%
  autoplot

# 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)
#>                     ME    RMSE      MAE       MPE     MAPE      MASE       ACF1
#> Training set 0.3576253 7.89734 5.788344 0.1458472 2.670181 0.1982148 0.05807465
# out-of-sample one-step forecasts.
accuracy(air.model2)
#>                     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
# out-of-sample multi-step 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