mat.ar3 {dae} R Documentation

## Forms an ar3 correlation matrix

### Description

Form the correlation matrix of order order whose correlations follow the ar3 pattern. The resulting matrix is banded.

### Usage

mat.ar3(ARparameters, order)

### Arguments

 ARparameters A numeric containing the three autoregressive parameter values of the process, being the weights given to the lag 1, lag 2 and lag 3 response values. order The order of the matrix to be formed.

### Details

The correlations in the correlation matrix, corr say, are calculated from the autoregressive parameters, ARparameters.
Let omega = 1 - ARparameters[2] - ARparameters[3] * (ARparameters[1] + ARparameters[3]). Then the values in

• the diagonal of corr (k = 1) are one;

• the first subdiagonal band (k = 2) of corr are equal to
(ARparameters[1] + ARparameters[2]*ARparameters[3]) / omega;

• the second subdiagonal band (k = 3) of corr are equal to
(ARparameters[1] * (ARparameters[1] + ARparameters[3]) +
ARparameters[2] * (1 - ARparameters[2])) / omega;

• the subsequent subdiagonal bands, (k = 4:order), of corr are equal to
ARparameters[1]*corr[k-1] + ARparameters[2]*corr[k-2] + ARparameters[3]*corr[k-3].

### Value

A banded correlation matrix whose elements follow an ar3 pattern.

Chris Brien