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

## Description

The function ltzb 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` ```ltzb(r,x) ```

## Arguments

 `r` autocorelation vector `x` time series data

## Value

Vector with values t(en) * solve(R) * x and t(en) * solve(R) * en. 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``` ```# Estimate the parameters for the Nile time series. r <- acfHKp(H = 0.8,maxlag = length(Nile)-1) examp <- ltzb(r,Nile) # Comparison of the algorithm with typical approaches examp[1] - as.numeric(t(rep(1,length(r))) %*% solve(toeplitz(r)) %*% Nile) examp[2] - as.numeric(t(rep(1,length(r))) %*% solve(toeplitz(r)) %*% rep(1,length(r))) ```

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