Library: | times |
See also: | hurst lo kpss |
Quantlet: | fracbrown | |
Description: | calculates the singular value decomposition of the covariance matrix of a fractional Brownian motion. |
Usage: | sv=fracbrown(p,nu,alpha) | |
Input: | ||
p | scalar, temporal scale factor | |
nu | scalar, the resulting matrix is a (2*p*nu+1) matrix | |
alpha | scalar, coefficient of the fractional Brownian motion | |
Output: | ||
sv | (2*p*nu+1)x(2*p*nu+1) matrix, singular value decomposition of the covariance matrix of a fractional Brownian motion with coefficient alpha |
v = sv*sv' ;
v[i,j] = (1/2)*(| s[i] |^alpha + | s[j] |^alpha - | s[i]-s[j] |^alpha), s=(-p*nu, ..., p*nu)
library("times") func("fracbrown.xpl") // load quantlet func("hurst.xpl") // load quantlet randomize(234) p=1 nu = 50 alpha = 1.5 // simulate frac. BM x=fracbrown(p,nu,alpha)*normal(2*p*nu+1) dim(x) // 2*p*nu+1 h=hurst(x,12) 2*h.b[2] // estimate alpha
Contents of dim [1,] 101 Contents of _tmp [1,] 1.5237