timsac (version 1.3.8)

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)

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.

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.

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