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

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 6.1.1-7
Package Index