| ar {stats} | R Documentation |
Fit an autoregressive time series model to the data, by default selecting the complexity by AIC.
ar(x, aic = TRUE, order.max = NULL,
method=c("yule-walker", "burg", "ols", "mle", "yw"), na.action,
series, ...)
ar.burg(x, ...)
## Default S3 method:
ar.burg(x, aic = TRUE, order.max = NULL,
na.action = na.fail, demean = TRUE, series, var.method = 1, ...)
## S3 method for class 'mts':
ar.burg(x, aic = TRUE, order.max = NULL,
na.action = na.fail, demean = TRUE, series, var.method = 1, ...)
ar.yw(x, ...)
## Default S3 method:
ar.yw(x, aic = TRUE, order.max = NULL,
na.action = na.fail, demean = TRUE, series, ...)
## S3 method for class 'mts':
ar.yw(x, aic = TRUE, order.max = NULL,
na.action = na.fail, demean = TRUE, series, ...)
ar.mle(x, aic = TRUE, order.max = NULL, na.action = na.fail, demean = TRUE,
series, ...)
## S3 method for class 'ar':
predict(object, newdata, n.ahead = 1, se.fit = TRUE, ...)
x |
A univariate or multivariate time series. |
aic |
Logical flag. If TRUE then the Akaike Information
Criterion is used to choose the order of the autoregressive
model. If FALSE, the model of order order.max is
fitted. |
order.max |
Maximum order (or order) of model to fit. Defaults
to 10*log10(N) where N is the number
of observations except for method="mle" where it is the
minimum of this quantity and 12. |
method |
Character string giving the method used to fit the
model. Must be one of the strings in the default argument
(the first few characters are sufficient). Defaults to
"yule-walker". |
na.action |
function to be called to handle missing values. |
demean |
should a mean be estimated during fitting? |
series |
names for the series. Defaults to
deparse(substitute(x)). |
var.method |
the method to estimate the innovations variance (see Details). |
... |
additional arguments for specific methods. |
object |
a fit from ar. |
newdata |
data to which to apply the prediction. |
n.ahead |
number of steps ahead at which to predict. |
se.fit |
logical: return estimated standard errors of the prediction error? |
For definiteness, note that the AR coefficients have the sign in
(x[t] - m) = a[1]*(x[t-1] - m) + ... + a[p]*(x[t-p] - m) + e[t]
ar is just a wrapper for the functions ar.yw,
ar.burg, ar.ols and ar.mle.
Order selection is done by AIC if aic is true. This is
problematic, as of the methods here only ar.mle performs
true maximum likelihood estimation. The AIC is computed as if the variance
estimate were the MLE, omitting the determinant term from the
likelihood. Note that this is not the same as the Gaussian likelihood
evaluated at the estimated parameter values. In ar.yw the
variance matrix of the innovations is computed from the fitted
coefficients and the autocovariance of x.
ar.burg allows two methods to estimate the innovations
variance and hence AIC. Method 1 is to use the update given by
the Levinson-Durbin recursion (Brockwell and Davis, 1991, (8.2.6)
on page 242), and follows S-PLUS. Method 2 is the mean of the sum
of squares of the forward and backward prediction errors
(as in Brockwell and Davis, 1996, page 145). Percival and Walden
(1998) discuss both. In the multivariate case the estimated
coefficients will depend (slightly) on the variance estimation method.
Remember that ar includes by default a constant in the model, by
removing the overall mean of x before fitting the AR model,
or (ar.mle) estimating a constant to subtract.
For ar and its methods a list of class "ar" with
the following elements:
order |
The order of the fitted model. This is chosen by
minimizing the AIC if aic=TRUE, otherwise it is order.max. |
ar |
Estimated autoregression coefficients for the fitted model. |
var.pred |
The prediction variance: an estimate of the portion of the variance of the time series that is not explained by the autoregressive model. |
x.mean |
The estimated mean of the series used in fitting and for use in prediction. |
x.intercept |
(ar.ols only.) The intercept in the model for
x - x.mean. |
aic |
The value of the aic argument. |
n.used |
The number of observations in the time series. |
order.max |
The value of the order.max argument. |
partialacf |
The estimate of the partial autocorrelation function
up to lag order.max. |
resid |
residuals from the fitted model, conditioning on the
first order observations. The first order residuals
are set to NA. If x is a time series, so is resid. |
method |
The value of the method argument. |
series |
The name(s) of the time series. |
asy.var.coef |
(univariate case.) The asymptotic-theory variance matrix of the coefficient estimates. |
For predict.ar, a time series of predictions, or if
se.fit = TRUE, a list with components pred, the
predictions, and se, the estimated standard errors. Both
components are time series.
Only the univariate case of ar.mle is implemented.
Fitting by method="mle" to long series can be very slow.
Martyn Plummer. Univariate case of ar.yw, ar.mle
and C code for univariate case of ar.burg by B. D. Ripley.
Brockwell, P. J. and Davis, R. A. (1991) Time Series and Forecasting Methods. Second edition. Springer, New York. Section 11.4.
Brockwell, P. J. and Davis, R. A. (1996) Introduction to Time Series and Forecasting. Springer, New York. Sections 5.1 and 7.6.
Percival, D. P. and Walden, A. T. (1998) Spectral Analysis for Physical Applications. Cambridge University Press.
Whittle, P. (1963) On the fitting of multivariate autoregressions and the approximate canonical factorization of a spectral density matrix. Biometrika 40, 129–134.
ar.ols, arima0 for ARMA models.
data(lh) ar(lh) ar(lh, method="burg") ar(lh, method="ols") ar(lh, FALSE, 4) # fit ar(4) data(sunspot) (sunspot.ar <- ar(sunspot.year)) predict(sunspot.ar, n.ahead=25) ## try the other methods too data(BJsales) ar(ts.union(BJsales, BJsales.lead)) ## Burg is quite different here, as is OLS (see ar.ols) ar(ts.union(BJsales, BJsales.lead), method="burg")