dae (version 3.2.21)

mat.ar3: 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)

Value

A banded correlation matrix whose elements follow an ar3 pattern.

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.

Author

Chris Brien

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].

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)