ar.ols                 package:stats                 R Documentation

Fit Autoregressive Models to Time Series by OLS

Description:

     Fit an autoregressive time series model to the data by ordinary
     least squares, by default selecting the complexity by AIC.

Usage:

     ar.ols(x, aic = TRUE, order.max = NULL, na.action = na.fail,
            demean = TRUE, intercept = demean, series, ...)

Arguments:

       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.

na.action: function to be called to handle missing values.

  demean: should the AR model be for 'x' minus its mean?

intercept: should a separate intercept term be fitted?

  series: names for the series.  Defaults to 'deparse(substitute(x))'.

     ...: further arguments to be passed to or from methods.

Details:

     '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.

Value:

     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 (or zero if 'demean' is false) of the
          series used in fitting and for use in prediction.

x.intercept: The intercept in the model for 'x - x.mean', or zero if
          'intercept' is false.

     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: 'NULL'.  For compatibility with 'ar'.

   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 character string '"Unconstrained LS"'.

  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.

Author(s):

     Adrian Trapletti, Brian Ripley.

References:

     Luetkepohl, H. (1991): _Introduction to Multiple Time Series
     Analysis._ Springer Verlag, NY, pp. 368-370.

See Also:

     'ar'

Examples:

     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)

