[SciPy-User] how to use signal.lfiltic?
Skipper Seabold
between signal processing language and time series econometrics.
I don't see how to use lfiltic.
Say I have a (known) output vector of errors and an input y vector. y
follows a mean zero ARMA(p,q) process given by b and a below where p =
q = 2. If I want to use lfilter to recreate the errors, forcing the
first p outputs (errors) to be zero, then I need to solve the
difference equations for the zi that do this which is given by zi
below. But if I try to recreate this using lfiltic, it doesn't work.
Am I missing the intention of lfiltic? Matlab's documentation, which
a lot of the signal stuff seems to be taken from, suggests that y and
x in lfiltic need to be reversed, but this also doesn't give the zi I
want.
from scipy import signal
import numpy as np
errors = np.array([ 0., 0., 0.00903417, 0.89064639, 1.51665674])
y = np. array([-0.60177354, -1.60410646, -1.16619292, 0.44003132, 2.36214611])
b = np.array([ 1. , -0.8622494 , 0.34549996])
a = np.array([ 1. , 0.07918344, -0.81594865])
# zi I want to produce errors = 0,0,...
zi = np.zeros(2)
zi[0] = -b[0] * y[0]
zi[1] = -b[1] * y[0] - b[0] * y[1]
zi
# array([ 0.60177354, 1.08522758])
e = signal.lfilter(b, a, y, zi=zi)
e[0]
# array([ 0. , 0. , 0.00903417, 0.89064639, 1.51665674])
zi2 = signal.lfiltic(b,a, errors[:2], y[:2])
zi2
# array([-0.03533984, -0.20791273])
e2 = signal.lfilter(b, a, y, zi=zi2)
e2[0]
# array([-0.63711338, -1.24269149, -0.41241704, -0.0899541 , 1.25042151])
Skipper
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Skipper Seabold
Basically, I think this line in signal.lfiltic
for m in range(M):
zi[m] = sum(b[m+1:]*x[:M-m],axis=0)
should be
for m in range(M):
zi[m] = sum(-b[:m+1][::-1]*x[:m+1],axis=0)
I'm not sure about the next loop, since my output are zero, I didn't
have to solve for it.
Is this a bug or am I misunderstanding?
Skipper Seabold
Misunderstanding. Matlab gives the same thing, but I still don't
understand why lfiltic doesn't give the same zi that I used to
actually create the output.