unimar {timsac}R Documentation

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, tmp.file=NULL)

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.
tmp.file a character string naming a file written intermediate results of AR coefficients computation. If NULL (default) output no file.

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 Gaussian white noise with mean 0 and variance v.

AIC is defined by

AIC = nlog(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.

Value

mean mean.
var variance.
v innovation variance.
aic AIC(m) (m = 0,...,max.order).
aicmin minimum AIC.
daic AIC(m)-aicmin (m = 0,...,max.order).
order.maice order of minimum AIC.
v.maice innovation variance attained at "order.maice".
arcoef AR coefficients.

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

[Package timsac version 1.2.1 Index]