Simple AR fitting

This example demonstrates simple AR(p) fitting with the Yule Walker equations.

We start off with imports from numpy, matplotlib and import nitime.utils as well as nitime.algorithms:

import numpy as np
from matplotlib import pyplot as plt

from nitime import utils
from nitime import algorithms as alg

We define some variables, which will be used in generating the AR process:

npts = 2048*10
sigma = 1
drop_transients = 1024
coefs = np.array([0.9, -0.5])

This generates an AR(2) time series:

X, v, _ = utils.ar_generator(npts, sigma, coefs, drop_transients)

We use the plot_tseries function in order to visualize the process:

import nitime.timeseries as ts
from nitime.viz import plot_tseries

fig_noise = plot_tseries(ts.TimeSeries(v,sampling_rate=1000,time_unit='s'))
fig_noise.suptitle('noise')

fig_ar = plot_tseries(ts.TimeSeries(X,sampling_rate=1000,time_unit='s'))
fig_ar.suptitle('AR signal')

Now we estimate back the model parameters:

sigma_est, coefs_est = alg.yule_AR_est(X, 2, 2*npts, system=True)

plt.show()

Example source code

You can download the full source code of this example. This same script is also included in the Nitime source distribution under the doc/examples/ directory.