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

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)

### 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 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.
`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

[Package timsac version 1.3.6 Index]