Hello -

I have been staring at this problem for too long now, that I decided to ask …

I have a problem showing the stochastic kernel. I believe that I have done the right calculations, but am unable to show the resulting data in a graph. An empty graph appears … and then nothing … Anyone, please help.

import numpy as np

import matplotlib.pyplot as plt

from scipy.stats import norm

n = 1000

theta = 0.8

d = np.sqrt(1-theta**2)

def p(x,y):

"Stochastic kernel for the TAR model"

return norm().pdf((y-theta*np.abs(x))/d)/d

Z = norm().rvs(n)

X = np.empty(n)

for t in range(n-1):

X[t+1] = theta*np.abs(X[t])+d*Z[t+1]

n = len(X)

X = X.reshape((n, 1))

ys = np.linspace(-3,3,200)

k = len(ys)

ys = ys.reshape((1,k))

v = p(X,ys)

kernel = np.mean(v, axis=0)

h = len(kernel)

kernel = kernel.reshape((1,h))

fig, ax = plt.subplots(figsize=(10,7))

ax.plot(ys,kernel, ‘b-’, lw=2,alpha=0.6, label=‘look ahead estimate’)

plt.show()