ar.ols | R Documentation |
Fit an autoregressive time series model to the data by ordinary least squares, by default selecting the complexity by AIC.
ar.ols(x, aic = TRUE, order.max = NULL, na.action = na.fail, demean = TRUE, intercept = demean, series, ...)
x |
A univariate or multivariate time series. |
aic |
Logical flag. If |
order.max |
Maximum order (or order) of model to fit. Defaults to 10*log10(N) where N is the number of observations. |
na.action |
function to be called to handle missing values. |
demean |
should the AR model be for |
intercept |
should a separate intercept term be fitted? |
series |
names for the series. Defaults to
|
... |
further arguments to be passed to or from methods. |
ar.ols
fits the general AR model to a possibly non-stationary
and/or multivariate system of series x
. The resulting
unconstrained least squares estimates are consistent, even if
some of the series are non-stationary and/or co-integrated.
For definiteness, note that the AR coefficients have the sign in
(x[t] - m) = a[0] a[1]*(x[t-1] - m) … a[p]*(x[t-p] - m) e[t]
where a[0] is zero unless intercept
is true, and
m is the sample mean if demean
is true, zero
otherwise.
Order selection is done by AIC if aic
is true. This is
problematic, as ar.ols
does not perform
true maximum likelihood estimation. The AIC is computed as if
the variance estimate (computed from the variance matrix of the
residuals) 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.
Some care is needed if intercept
is true and demean
is
false. Only use this is the series are roughly centred on
zero. Otherwise the computations may be inaccurate or fail entirely.
A list of class "ar"
with the following elements:
order |
The order of the fitted model. This is chosen by
minimizing the AIC if |
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 (or zero if |
x.intercept |
The intercept in the model for
|
aic |
The differences in AIC between each model and the
best-fitting model. Note that the latter can have an AIC of |
n.used |
The number of observations in the time series. |
order.max |
The value of the |
partialacf |
|
resid |
residuals from the fitted model, conditioning on the
first |
method |
The character string |
series |
The name(s) of the time series. |
frequency |
The frequency of the time series. |
call |
The matched call. |
asy.se.coef |
The asymptotic-theory standard errors of the coefficient estimates. |
Adrian Trapletti, Brian Ripley.
Luetkepohl, H. (1991): Introduction to Multiple Time Series Analysis. Springer Verlag, NY, pp. 368–370.
ar
ar(lh, method = "burg") ar.ols(lh) ar.ols(lh, FALSE, 4) # fit ar(4) ar.ols(ts.union(BJsales, BJsales.lead)) x <- diff(log(EuStockMarkets)) ar.ols(x, order.max = 6, demean = FALSE, intercept = TRUE)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.