ltza | R Documentation |
The function ltza is used to calculate the value of quadratic forms for the inverse of a symmetric positive definite autocorrelation matrix, using the Levinson algorithm (Golub and Van Loan 1996, Algorithm 4.7.2).
ltza(r, x)
r |
autocorelation vector |
x |
time series data |
Vector with values t(x) * solve(R) * x, t(en) * solve(R) * x, t(en) * solve(R) * en and the natural logarithm of the determinant of R. t(.) denotes the transpose of a vector, en = (1,1,...,1) and R is the autocorrelation matrix.
Hristos Tyralis
Golub GH, Van Loan CF (1996) Matrix Computations. Baltimore: John Hopkins University Press.
# Estimate the parameters for the Nile time series. r <- acfHKp(H = 0.8, maxlag = length(Nile)-1) examp <- ltza(r, Nile) # Comparison of the algorithm with typical approaches examp[1] - as.numeric(t(Nile) %*% solve(toeplitz(r)) %*% Nile) examp[2] - as.numeric(t(rep(1, length(r))) %*% solve(toeplitz(r)) %*% Nile) examp[3] - as.numeric(t(rep(1, length(r))) %*% solve(toeplitz(r)) %*% rep(1,length(r))) examp[4] - log(det(toeplitz(r)))
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