timsac (version 1.3.0)

unimar: Univariate Case of Minimum AIC Method of AR Model Fitting

Description

This is the basic program for the fitting of autoregressive models of successively higher by the method of least squares realized through householder transformation.

Usage

unimar(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
  innovation variance attained at order.maice.
• arcoef
  AR coefficients.

Details

The AR model is given by $$y(t) = a(1)y(t-1) + \ldots + a(p)y(t-p) + u(t),$$ where $p$ is AR order and $u(t)$ is Gaussian white noise with mean $0$ and variance $v$. AIC is defined by $$AIC = n\log(det(v)) + 2k,$$ where $n$ is the length of data, $v$ is the estimates of the innovation variance and $k$ is the number of parameter.

References

G.Kitagawa and H.Akaike (1978) A Procedure For The Modeling of Non-Stationary Time Series. Ann. Inst. Statist. Math.,30, B, 351--363. 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 <- unimar(Canadianlynx, max.order=20)
  z$arcoef