
Fit an ARMA model to a univariate time series by conditional least
squares. For exact maximum likelihood estimation see
arima0
.
arma(x, order = c(1, 1), lag = NULL, coef = NULL,
include.intercept = TRUE, series = NULL, qr.tol = 1e-07, …)
a numeric vector or time series.
a two dimensional integer vector giving the orders of the
model to fit. order[1]
corresponds to the AR part and
order[2]
to the MA part.
a list with components ar
and ma
. Each
component is an integer vector, specifying the AR and MA lags that are
included in the model. If both, order
and lag
, are
given, only the specification from lag
is used.
If given this numeric vector is used as the initial estimate of the ARMA coefficients. The preliminary estimator suggested in Hannan and Rissanen (1982) is used for the default initialization.
Should the model contain an intercept?
name for the series. Defaults to
deparse(substitute(x))
.
the tol
argument for qr
when computing
the asymptotic standard errors of coef
.
additional arguments for optim
when fitting
the model.
A list of class "arma"
with the following elements:
the lag specification of the fitted model.
estimated ARMA coefficients for the fitted model.
the conditional sum-of-squared errors.
the number of observations of x
.
the series of residuals.
the fitted series.
the name of the series x
.
the frequency of the series x
.
the call of the arma
function.
estimate of the asymptotic-theory covariance matrix for the coefficient estimates.
The convergence
integer code from
optim
.
Does the model contain an intercept?
The following parametrization is used for the ARMA(p,q) model:
where lag
, it is possible to fit a parsimonious submodel
by setting arbitrary
arma
uses optim
to minimize the conditional
sum-of-squared errors. The gradient is computed, if it is needed, by
a finite-difference approximation. Default initialization is done by
fitting a pure high-order AR model (see ar.ols
).
The estimated residuals are then used for computing a least squares
estimator of the full ARMA model. See Hannan and Rissanen (1982) for
details.
E. J. Hannan and J. Rissanen (1982): Recursive Estimation of Mixed Autoregressive-Moving Average Order. Biometrika 69, 81--94.
summary.arma
for summarizing ARMA model fits;
arma-methods
for further methods;
arima0
, ar
.
# NOT RUN {
data(tcm)
r <- diff(tcm10y)
summary(r.arma <- arma(r, order = c(1, 0)))
summary(r.arma <- arma(r, order = c(2, 0)))
summary(r.arma <- arma(r, order = c(0, 1)))
summary(r.arma <- arma(r, order = c(0, 2)))
summary(r.arma <- arma(r, order = c(1, 1)))
plot(r.arma)
data(nino)
s <- nino3.4
summary(s.arma <- arma(s, order=c(20,0)))
summary(s.arma
<- arma(s, lag=list(ar=c(1,3,7,10,12,13,16,17,19),ma=NULL)))
acf(residuals(s.arma), na.action=na.remove)
pacf(residuals(s.arma), na.action=na.remove)
summary(s.arma
<- arma(s, lag=list(ar=c(1,3,7,10,12,13,16,17,19),ma=12)))
summary(s.arma
<- arma(s, lag=list(ar=c(1,3,7,10,12,13,16,17),ma=12)))
plot(s.arma)
# }
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