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

In timsac: Time Series Analysis and Control Package

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.

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.

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.

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

timsac documentation built on Sept. 30, 2023, 5:06 p.m.