Recursion: IIR filter with `scipy.lfilter`

Question

Given some data x:

from pandas_datareader.data import DataReader as dr
x = np.squeeze(dr(\'DTWEXB\', \'fred\').dropna().values)

I

Answer 1

Take the z-transform of your filter, that gives you the values for the numerator b and denominator a:

       alpha
y(z) = ------------------ x(z)
       1 - (1-alpha) z^-1

So you run

import scipy.signal
x[0] /= alpha
y = scipy.signal.lfilter([alpha], [1, - 1 + alpha], x)

Which yields

array([ 101.1818    ,  101.176862  ,  101.16819314, ...,  120.9813121 ,
        120.92484874,  120.85786628])

Note I have scaled x[0] to account for the initial condition you wanted.