timsac (version 1.3.0)

exsar: Exact Maximum Likelihood Method of Scalar AR Model Fitting

Description

Produce exact maximum likelihood estimates of the parameters of a scalar AR model.

Usage

exsar(y, max.order=NULL, plot=FALSE)

Arguments

y

a univariate time series.

max.order

upper limit of AR order. Default is $2 \sqrt{n}$, where $n$ is the length of the time series y.

plot

logical. If TRUE daic is plotted.

Value

• mean
  mean.
• var
  variance.
• v
  innovation variance.
• aic
  AIC.
• aicmin
  minimum AIC.
• daic
  AIC-aicmin.
• order.maice
  order of minimum AIC.
• v.maice
  MAICE innovation variance.
• arcoef.maice
  MAICE AR coefficients.
• v.mle
  maximum likelihood estimates of innovation variance.
• arcoef.mle
  maximum likelihood estimates of AR coefficients.

Details

The AR model is given by $$y(t) = a(1)y(t-1) + .... + a(p)y(t-p) + u(t)$$ where $p$ is AR order and $u(t)$ is a zero mean white noise.

References

H.Akaike, G.Kitagawa, E.Arahata and F.Tada (1979) Computer Science Monograph, No.11, Timsac78. The Institute of Statistical Mathematics.

Examples

data(Canadianlynx)
  z <- exsar(Canadianlynx, max.order=14)
  z$arcoef.maice
  z$arcoef.mle