# -*- coding: utf-8 -*-
"""
Created on Sat Nov 01 13:02:50 2014@author: dell
"""import pandas, numpy as np
ewma = pandas.stats.moments.ewma
import matplotlib.pyplot as plt# make a hat function, and add noise
x = np.linspace(0,1,100)
x = np.hstack((x,x[::-1]))
x += np.random.normal( loc=0, scale=0.1, size=200 ) plt.plot( x, alpha=0.4, label='Raw' ) # take EWMA in both directions with a smaller span term fwd = ewma( x, span=15 ) # take EWMA in fwd direction bwd = ewma( x[::-1], span=15 ) # take EWMA in bwd direction c = np.vstack(( fwd, bwd[::-1] )) # lump fwd and bwd together c = np.mean( c, axis=0 ) # average # regular EWMA, with bias against trend plt.plot( ewma( x, span=20 ), 'b', label='EWMA, span=20' ) # "corrected" (?) EWMA plt.plot( c, 'r', label='Reversed-Recombined' ) plt.legend(loc=8) plt.savefig( 'ewma_correction.png', fmt='png', dpi=100 )

# -*- coding: utf-8 -*-
"""
Created on Sat Nov 01 14:10:05 2014@author: dell
"""import numpy as np
import matplotlib.pyplot as pltdef holt_winters_second_order_ewma( x, span, beta ):N = x.sizealpha = 2.0 / ( 1 + span )s = np.zeros(( N, )) b = np.zeros(( N, )) s[0] = x[0] for i in range( 1, N ): s[i] = alpha * x[i] + ( 1 - alpha )*( s[i-1] + b[i-1] ) b[i] = beta * ( s[i] - s[i-1] ) + ( 1 - beta ) * b[i-1] return s # make a hat function, and add noise x = np.linspace(0,1,100) x = np.hstack((x,x[::-1])) x += np.random.normal( loc=0, scale=0.1, size=200 ) + 3.0 plt.plot( x, alpha=0.4, label='Raw' ) # holt winters second order ewma plt.plot( holt_winters_second_order_ewma( x, 10, 0.3 ), 'b', label='Holt-Winters' ) plt.title('Holt-Winters' ) plt.legend( loc=8 ) plt.savefig( 'holt_winters.png', fmt='png', dpi=100 )