timsac (version 1.3.8)

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)

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.

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

$$y(t) = a(1)y(t-1) + .... + a(p)y(t-p) + u(t)$$

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