https://www.sarem-seitz.com/winning-with-simple-not-even-linear-time-series-models

cauchy_memory.py

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(987)

#cauchy distribution is equivalent to a Student-T with 1 degree of freedom
#see https://stats.stackexchange.com/questions/151854/a-normal-divided-by-the-sqrt-chi2s-s-gives-you-a-t-distribution-proof
heavy_tailed_noise = np.random.normal(size = (120))/np.sqrt(np.random.normal(size = (120))**2)
seasonal_series = np.cumsum(heavy_tailed_noise.reshape((10,12)),0).reshape(-1)

fig, axs = plt.subplots(figsize = (24,8), nrows=1, ncols=2)


axs[0].plot(heavy_tailed_noise,color="blue")
axs[0].margins(x=0)
axs[0].grid(alpha=0.5)

axs[1].plot(seasonal_series,color="blue")
axs[1].margins(x=0)
axs[1].grid(alpha=0.5)