def denoise_OL(S, do_plot=True):
np.argwhere(np.isnan(S))
# cor.shape = (1000,1000). If rowvar=1 - row represents a var, with observations in the columns.
cor = np.corrcoef(S, rowvar=0)
eVal0, eVec0 = mp.getPCA(cor)
print(np.argwhere(np.isnan(np.diag(eVal0))))
# code snippet 2.4
q = float(S.shape[0]) / S.shape[1] #T/N
eMax0, var0 = mp.findMaxEval(np.diag(eVal0), q, bWidth=.01)
nFacts0 = eVal0.shape[0] - np.diag(eVal0)[::-1].searchsorted(eMax0)
if do_plot:
fig = plt.figure()
ax = fig.add_subplot(111)
ax.hist(np.diag(eVal0), density=True,
bins=100) #, normed = True) #normed = True,
pdf0 = mp.mpPDF(var0, q=S.shape[0] / float(S.shape[1]), pts=N)
pdf1 = mp.fitKDE(np.diag(eVal0), bWidth=.005) #empirical pdf
#plt.plot(pdf1.keys(), pdf1, color='g') #no point in drawing this
plt.plot(pdf0.keys(), pdf0, color='r')
plt.show()
# code snippet 2.5 - denoising by constant residual eigenvalue
corr1 = mp.denoisedCorr(eVal0, eVec0, nFacts0)
eVal1, eVec1 = mp.getPCA(corr1)
return eVal0, eVec0, eVal1, eVec1, corr1, var0
def deNoiseCov(cov0, q, bWidth):
corr0 = mp.cov2corr(cov0)
eVal0, eVec0 = mp.getPCA(corr0)
eMax0, var0 = mp.findMaxEval(np.diag(eVal0), q, bWidth)
nFacts0 = eVal0.shape[0]-np.diag(eVal0)[::-1].searchsorted(eMax0)
corr1 = mp.denoisedCorr(eVal0, eVec0, nFacts0) #denoising by constant residual eigenvalue method
cov1 = corr2cov(corr1, np.diag(cov0)**.5)
return cov1
# use matrix of returns to calc correlation
S, instrument_returns = calculate_returns(S_value)
_, instrument_returns = calculate_returns(S_value,
percentageAsProduct=True)
#S = S_value
#print performance ascending
print(np.asarray(portfolio_name)[np.argsort(instrument_returns)])
#calculate_correlation(S)
eVal0, eVec0, denoised_eVal, denoised_eVec, denoised_corr, var0 = denoise_OL(
S)
detoned_corr = mp.detoned_corr(denoised_corr,
denoised_eVal,
denoised_eVec,
market_component=1)
detoned_eVal, detoned_eVec = mp.getPCA(detoned_corr)
denoised_eigenvalue = np.diag(denoised_eVal)
eigenvalue_prior = np.diag(eVal0)
plt.plot(range(0, len(denoised_eigenvalue)),
np.log(denoised_eigenvalue),
color='r',
label="Denoised eigen-function")
plt.plot(range(0, len(eigenvalue_prior)),
np.log(eigenvalue_prior),
color='g',
label="Original eigen-function")
plt.xlabel("Eigenvalue number")
plt.ylabel("Eigenvalue (log-scale)")
plt.legend(loc="upper right")
plt.show()