arima
ARIMA Modelling of Time Series

### Description

Fits an ARIMA (auto-regressive integrated moving average) mode to a time series.

### Usage

    arima(x, order = c(0, 0, 0), seasonal = list(order = c(0, 0, 0), period = NA),
          xreg = NULL, include.mean = TRUE, transform.pars = TRUE, fixed = NULL,
          init = NULL, method = c("CSS-ML", "ML", "CSS"), n.cond,
          SSinit, optim.method = "BFGS",
          optim.control = list(), kappa = 1e+06)
    ## S3 method for class 'Arima2':
    print(x, ...)
    ## S3 method for class 'Arima2':
    coef(object, ...)
    ## S3 method for class 'Arima2':
    vcov(object, ...)

### Arguments

x | a numeric vector or univariate time series.
order | a three-long integer vector giving the number of autoregressive parameters to fit, the number of difference operations to perform, and the number of moving average parameters to fit.
seasonal | a list with two components describing the seasonal part of the model: order is a three-long integer vector describing the order of the seasonal ARIMA model and period is an integer specifying the number of observations in the cyclical time period. If period is NA or not in the list, then it is set to frequency(x). seasonal can also be just the order vector from the above list and the period is set to frequency(x).
xreg | a time series, a vector, or a matrix of regressors. If x and xreg are both time series, they should have the same frequency. If they have different start or end times, the fitting takes place on the intersection of their time spans.
include.mean | a logical value. If TRUE (the default) and if there are no differencing terms in the model, then a column of 1s is included in xreg so the mean is estimated.
transform.pars | This argument is ignored.
fixed | This argument is ignored.
init | This argument is ignored.
method | This argument is ignored.
n.cond | This argument is ignored.
SSinit | This argument is ignored.
optim.method | This argument is ignored. The likelihood is optimized using optim(method="L-BFGS-B").
optim.control | This argument is ignored.
kappa | This argument is ignored.

### Details

- For model identification see acf and pacf.
- for creating a sample ARIMA process, see arima.sim.
- For quickly fitting AR processes with automatic order selection, see ar.

Value
arima() returns an object of class "Arima2" (different than that of R and S-PLUS), which is a list with the following components:

coef | The estimated nonseasonal and seasonal ar and ma coefficients.
loglik | The logarithm of the likelihood evaluated at the above coefficients.
sigma2 | The estimated innovation variance.
aic | Akaite's information criterion for this fitted model.
n.used | The number of observations used in making the estimates.
n.cond | The number of initial observations that the likelihood is conditional on.
reg.coef | The estimated coefficients of the regressor columns, including the intercept if the mean is included in the model. This component is omitted if there are no regressors.
ier | Currently this is a meaningless integer.
model | A description of the fitted model in the format and parameterization used by S-PLUS.
call | A function call that can refit this model.
series | The name of the input series, x.
seriesData | The input series itself.
xreg | The regressors. This component is omitted if there are no regressors.
var.coef | The variance matrix of the estimated ar and ma coefficients.

The coef method for Arima2 objects returns the ar, ma, and regression coefficients as a single labelled vector.
The vcov method for Arima2 objects returns the variance matrix of the ar and ma estimates, but not for the regression coefficients.
References
Ansley, C. F. 1979. An algorithm for the exact likelihood of a mixed autoregressive-moving average process. Biometrika. Volume 66. 59-65.
Kohn, R. and Ansley, C. F. 1985. Efficient estimation and prediction in time series regression models. Biometrika. Volume 72. 694-697.
Bell, W. and Hillmer, S. 1987. Initializing the Kalman filter in the nonstationary case. Research Report CENSUS/SRC/RR-87/33. Washington, DC: Statistical Research Division, Bureau of the Census. 20233
Gardner, G., Harvey, A. C., and Phillips, G. D. A. 1980. Algorithm AS154. An algorithm for exact maximum likelihood estimation of autoregressive-moving average models by means of Kalman filtering. Applied Statistics. Volume 29. 311-322.
Kohn, R. and Ansley, C. F. 1986. Estimation, prediction, and interpolation for ARIMA models with missing data. Journal of the American Statistical Association.
Jones, R. H. 1980. Maximum likelihood fitting of ARMA models to time series with missing observations. Technometrics. Volume 22. 389-395.
See Also
acf, pacf, arima.sim, ar
Examples

    fit <- arima(co2, order=c(1,1,1), seasonal=c(1,1,2))
    print(fit)
    vcov(fit)
    predict(fit, n.ahead=12)

Package stats version 6.1.5-18
Package Index