How to predict time series in scikit-learn?

This might be what you're looking for, with regard to the exponentially weighted moving average:

import pandas, numpy
ewma = pandas.stats.moments.ewma
EMOV_n = ewma( ys, com=2 )

Here, com is a parameter that you can read about here. Then you can combine EMOV_n to Xs, using something like:

Xs = numpy.vstack((Xs,EMOV_n))

And then you can look at various linear models, here, and do something like:

from sklearn import linear_model
clf = linear_model.LinearRegression()
clf.fit ( Xs, ys )
print clf.coef_

Best of luck!

According to Wikipedia, EWMA works well with stationary data, but it does not work as expected in the presence of trends, or seasonality. In those cases you should use a second or third order EWMA method, respectively. I decided to look at the pandas ewma function to see how it handled trends, and this is what I came up with:

import pandas, numpy as np
ewma = pandas.stats.moments.ewma

# 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 )
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
plot( ewma( x, span=20 ), 'b', label='EWMA, span=20' )

# "corrected" (?) EWMA
plot( c, 'r', label='Reversed-Recombined' )

legend(loc=8)
savefig( 'ewma_correction.png', fmt='png', dpi=100 )

As you can see, the EWMA bucks the trend uphill and downhill. We can correct for this (without having to implement a second-order scheme ourselves) by taking the EWMA in both directions and then averaging. I hope your data was stationary!