mat.ar3: Forms an ar3 correlation matrix

In dae: Functions Useful in the Design and ANOVA of Experiments

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.

Author(s)

Chris Brien

See Also

mat.I, mat.J, mat.cor, mat.corg, mat.banded, mat.exp, mat.gau, mat.ar1, mat.ar2, mat.sar2, mat.ma1, mat.ma2, mat.arma

Examples

    corr <- mat.ar3(ARparameters = c(0.4, 0.2, 0.1), order = 4)

dae documentation built on Aug. 21, 2025, 5:56 p.m.