advanced-algorithmic-trading

62
changes as the number of degrees-of-freedom are increased. Notice that the kurtosis becomes
smaller–the tails become less "fat"–representing lesser likelihood of more extreme events:
# student_t_plot.py
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import t
import seaborn as sns
if __name__ == "__main__":
sns.set_palette("deep", desat=.6)
sns.set_context(rc={"figure.figsize": (8, 4)})
x = np.linspace(-5.0, 5.0, 100)
nus = [1.0, 2.0, 5.0, 50.0]
for nu in nus:
y = t.pdf(x, nu)
ax = plt.plot(x, y, label="$\\nu=%s$" % nu)
plt.xlabel("x")
plt.ylabel("P(x)")
plt.legend(title="Parameters")
plt.show()
Figure 6.2: Different realisations of Student’s t-distribution for various parameters ν.
The degrees of freedom of the Student’s t–how much kurtosis it possesses–is governed by the
ν parameter described above: