# ltza: Value of quadratic forms for the inverse of a symmetric... In HKprocess: Hurst-Kolmogorov Process

## Description

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).

## Usage

 `1` ```ltza(r,x) ```

## Arguments

 `r` autocorelation vector `x` time series data

## Value

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

## References

Golub G.H., Van Loan C.F. (1996) Matrix Computations, Baltimore: John Hopkins University Press.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```# 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))) ```

HKprocess documentation built on May 29, 2017, 9:20 p.m.