Form the correlation matrix of order order whose
correlations follow the ar3 pattern. The resulting matrix
is banded.
mat.ar3(ARparameters, order)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.
The order of the matrix to be formed.
A banded correlation matrix whose elements follow an ar3 pattern.
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].
mat.I, mat.J, mat.banded, mat.exp, mat.gau,
mat.ar1, mat.ar2, mat.sar2,
mat.ma1, mat.ma2, mat.arma
# NOT RUN {
corr <- mat.ar3(ARparameters = c(0.4, 0.2, 0.1), order = 4)
# }
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