FRACLAB Functions |
![]() ![]() |
Generates an Alpha-Stable Linear Fractional Motion
ASM = asmlinfrac(N,ALPHA,H,M,m)
ASM = asmlinfrac(...,SEED)
ASM = asmlinfrac(N,ALPHA,H,M,m) Generates the alpha-stable linear fractional motion, ASM, using a sample size, N, a stability parameter, ALPHA, a self-similirity parameter, H, a kernel cut-off parameter, M and a number of discretization steps, m. The parameters N,M and m are positive integers and this triplet should be chosen so that the value m*(N+2*M) is a power of 2. ALPHA is a real in (0,2) and H must be a real in (0,1) different to (1/ALPHA).
ASM = asmlinfrac(...,SEED) Generates the alpha-stable linear fractional motion, ASM, with a specific random seed, SEED. This is useful to generate the same path several times or to compare the paths of different ASMs.
N = 1000; A = 1.5; H = 0.5; M = 12; m = 32; t = linspace(0,1,N);
asm = asmlinfrac(N,A,H,M,m);
figure; plot(t,asm);
title('Linear Fractional Motion with alpha = 1.5 and H = 0.5'); xlabel('time')
N = 2000; A1 = 1.5; A2 = 1.8; H = 0.5; M = 24; m = 32;
asm1 = asmlinfrac(N,A1,H,M,m,25);
asm2 = asmlinfrac(N,A2,H,M,m,25);
figure; plot(asm1,'k'); hold on; plot(asm2,'r');
legend('asm1: alpha = 1.5','asm2: alpha = 1.8','Location','NorthWest');
title('Linear Fractional Motion with different values of alpha parameter');
xlabel('number of points');xlim([0 N])
asmlevy, asmornhulen, msmlinmfrac
[1] S. Stoev, M. Taqqu "Simulation methods for linear fractional stable motion and FARIMA using the Fast Fourier Transform", Fractals, Vol. 12, No. 1 (2004) 95-121.
[2] K. Falconer, R. Le Guével, J. Lévy Véhel "Localisable moving average stable and multistable processes", Stochastic Models.
![]() |
asmlevy | asmornhulen | ![]() |