Many natural phenomena are regular and trustworthy like an accurate clock. Some phenomena exhibit patterns that seem regular. A group of scientists found three cycles in the sunspot activity with the Hilbert-Huang transform (see http://en.wikipedia.org/wiki/Hilbert%E2%80%93Huang_transform). The cycles have a duration of 11, 22, and 100 years approximately. Normally, we would simulate a periodic signal using trigonometric functions such as a sine function. You probably remember a bit of trigonometry from high school. That's all we need for this example. Since we have three cycles, it seems reasonable to create a model, which is a linear combination of three sine functions. This just requires a tiny adjustment of the code for the autoregressive model. Refer to the periodic.py file in this book's code bundle for the following code:

from scipy.optimize import leastsq
import statsmodels.api as sm
import matplotlib.pyplot as plt
import numpy as np
def model(p, t):
...