arma {tseries} | R Documentation |
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, ...)
x |
a numeric vector or time series. |
order |
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. |
lag |
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. |
coef |
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. |
include.intercept |
Should the model contain an intercept? |
series |
name for the series. Defaults to
deparse(substitute(x)) . |
qr.tol |
the tol argument for qr when computing
the asymptotic standard errors of coef . |
... |
additional arguments for optim when fitting
the model. |
The following parametrization is used for the ARMA(p,q) model:
y[t] = a[0] + a[1]y[t-1] + ... + a[p]y[t-p] + b[1]e[t-1] + ... + b[q]e[t-q] + e[t],
where a[0] is set to zero if no intercept is included. By using
the argument lag
, it is possible to fit a parsimonious submodel
by setting arbitrary a[i] and b[i] to zero.
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.
A list of class "arma"
with the following elements:
lag |
the lag specification of the fitted model. |
coef |
estimated ARMA coefficients for the fitted model. |
css |
the conditional sum-of-squared errors. |
n.used |
the number of observations of x . |
residuals |
the series of residuals. |
fitted.values |
the fitted series. |
series |
the name of the series x . |
frequency |
the frequency of the series x . |
call |
the call of the arma function. |
asy.se.coef |
the asymptotic-theory standard errors of the coefficient estimates. |
convergence |
The convergence integer code from
optim . |
include.intercept |
Does the model contain an intercept? |
A. Trapletti
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
.
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)