How to predict time series in scikit-learn?

Question

Scikit-learn utilizes a very convenient approach based on fit and predict methods. I have time-series data in the format suited for fit

Answer 1

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!

Answer 2

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!