from matplotlib.finance import quotes_historical_yahoo
import numpy as np
import matplotlib.pyplot as plt
from scipy import fftpack
from scipy import signal
from matplotlib.dates import DateFormatter
from matplotlib.dates import DayLocator
from matplotlib.dates import MonthLocator
from scipy import optimize


start = (2010, 7, 25)
end = (2011, 7, 25)

quotes = quotes_historical_yahoo("QQQ", start, end)
quotes = np.array(quotes)

dates = quotes.T[0]
qqq = quotes.T[4]


y = signal.detrend(qqq)


alldays = DayLocator()              
months = MonthLocator()
month_formatter = DateFormatter("%b %Y")

fig = plt.figure()
fig.subplots_adjust(hspace=.3)
ax = fig.add_subplot(211)

ax.xaxis.set_minor_locator(alldays)
ax.xaxis.set_major_locator(months)
ax.xaxis.set_major_formatter(month_formatter)
ax.tick_params(axis='both', which='major', labelsize='x-large')

amps = np.abs(fftpack.fftshift(fftpack.rfft(y)))
amps[amps < amps.max()] = 0

def residuals(p, y, x):
   A,k,theta,b = p
   err = y-A * np.sin(2* np.pi* k * x + theta) + b

   return err

filtered = -fftpack.irfft(fftpack.ifftshift(amps))
N = len(qqq)
f = np.linspace(-N/2, N/2, N)
p0 = [filtered.max(), f[amps.argmax()]/(2*N), 0, 0]
print "P0", p0

plsq = optimize.leastsq(residuals, p0, args=(filtered, dates))
p = plsq[0]
print "P", p
plt.plot(dates, y, 'o', label="detrended")
plt.plot(dates, filtered, label="filtered")
plt.plot(dates, p[0] * np.sin(2 * np.pi * dates * p[1] + p[2]) + p[3], '^', label="fit")
fig.autofmt_xdate()
plt.legend(prop={'size':'x-large'})

ax2 = fig.add_subplot(212)
ax2.tick_params(axis='both', which='major', labelsize='x-large')
plt.plot(f, amps, label="transformed")

plt.legend(prop={'size':'x-large'})
plt.show()