def plot_syj_against_j(j1=2, j2=6, wtype=1, theoretical_Hurst=0.8, idx_simulation=0, OUTPUT_FILE=None):
idx = int(theoretical_Hurst * 10) - 1
if(idx < 0 or idx > 10):
idx = 7
simulation = np.cumsum(opas.get_simulation(), axis=-1)
dico = wtspecq_statlog3(simulation[idx,idx_simulation], 2, 1, np.array(2),
int(np.log2(simulation[idx,idx_simulation].shape[0])), 0, 0)
Elog = dico['Elogmuqj'][0]
Varlog = dico['Varlogmuqj'][0]
nj = dico['nj']
regression = regrespond_det2(Elog, Varlog, nj, j1, j2, wtype)
font = {'family' : 'normal',
'weight' : 'bold',
'size' : 22}
changefont('font', **font)
jmax = len(Elog)
j_indices = np.arange(0,jmax + 2)
fig = plt.plot(j_indices, j_indices * regression['Zeta'] + regression['aest'])
plt.text(j_indices.mean() - 2 * j_indices.var() / jmax, Elog.mean() + Elog.var() / jmax, r'Hurst Exponent = %.2f'%(regression['Zeta']/2))
j_indices = np.arange(0,jmax) + 1
plt.plot(j_indices, Elog, 'ro')
plt.xlabel('scale j')
plt.ylabel('log Sy(j,2)')
if not OUTPUT_FILE is None:
plt.savefig(OUTPUT_FILE)
plt.show()
def compute_estimators(length_simul):
simulations = opas.get_simulation()[:,:,:length_simul]
shape = (9, 1000, length_simul)
simulations = np.reshape(simulations, (9000, length_simul))
N = simulations.shape[0]
wavelet_estim = np.zeros(N)
nb_vanishmoment = 2
j1 = 2
j2 = 6
wtype = 1
simulationsCS = np.cumsum(simulations, axis=-1)
dico = wtspecq_statlog32(simulationsCS, nb_vanishmoment, 1, np.array(2),
int(np.log2(length_simul)), 0, 0)
Elog = dico['Elogmuqj'][:, 0]
Varlog = dico['Varlogmuqj'][:, 0]
nj = dico['nj']
for j in np.arange(0, N):
sortie = regrespond_det2(Elog[j], Varlog[j], 2, nj, j1, j2, wtype)
wavelet_estim[j] = sortie['Zeta'] / 2.
wavelet_estim = np.reshape(wavelet_estim, shape[:-1])
welch_estim = welch_estimator(simulations)
welch_estim = np.reshape(welch_estim, shape[:-1])
dfa_estim = hurstexp_dfa(simulations, CumSum=1)
dfa_estim = np.reshape(dfa_estim, shape[:-1])
return wavelet_estim, welch_estim, dfa_estim
def compute_dfa_estimators(length_simul=4069, printout=0):
simulations = opas.get_simulation()[:,:,:length_simul]
shape = (9, 1000, length_simul)
simulations = np.reshape(simulations, (9000, length_simul))
N = simulations.shape[0]
j1 = 2
j2 = 6
wtype = 1
dfa_estim, dico = hurstexp_dfa(simulations, CumSum=1, polyfit=1)
dfa_estim1, dico = hurstexp_dfa(simulations, CumSum=1)
dfa_estim2, dico = hurstexp_dfa(simulations, CumSum=1, wtype=0)
k = 0
if printout!=0:
f, myplot = plt.subplots(1, 3, sharey=True)
f.suptitle('Estimation of Hurst coefficient of fGn\nof length 514 by dfa implementation')
for idx_subplot, (title, stat) in enumerate(zip(['dfa0', 'dfa1', 'dfa2'], [np.reshape(dfa_estim, shape[:-1]),
np.reshape(dfa_estim1, shape[:-1]),
np.reshape(dfa_estim2, shape[:-1])])):
myplot[idx_subplot].set_title(title)
bp = myplot[idx_subplot].boxplot(stat.T)
for line in bp['medians']:
x, y = line.get_xydata()[1]
if(k <6):
myplot[idx_subplot].text(x + 1.5, y - 0.02, '%.3f\n%.3e' % (np.mean(stat[k, :]),
np.var(stat[k,:])),
horizontalalignment='center')
else:
myplot[idx_subplot].text(x - 2, y - 0.02, '%.3f\n%.3e' % (np.mean(stat[k, :]),
np.var(stat[k, :])),
horizontalalignment='center')
k += 1
k = 0
plt.show()
return dfa_estim, dfa_estim1, dfa_estim2