Chapter 2. Univariate Volatility Modeling (in MATLAB/Python)

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Listing 2.1/2.2: ARCH and GARCH estimation in MATLAB Last updated June 2018

y=diff(log(p))*100;
y=y-mean(y);
%% We multiply returns by 100 and de-mean them
tarch(y,1,0,0);      % ARCH(1)
tarch(y,4,0,0);      % ARCH(4)
tarch(y,4,0,1);      % GARCH(4,1)
tarch(y,1,0,1);      % GARCH(1,1)
tarch(y,1,0,1,'STUDENTST'); % t-GARCH(1,1)

Listing 2.1/2.2: ARCH and GARCH estimation in Python Last updated July 2020

import numpy as np
p = np.loadtxt('index.csv', delimiter = ',', skiprows = 1)
y = np.diff(np.log(p), n=1, axis=0)*100
y = y-np.mean(y)
from arch import arch_model
## using Kevin Sheppard's ARCH package for Python
## ARCH(1)
am = arch_model(y, mean = 'Zero', vol='Garch', p=1, o=0, q=0, dist='Normal')
arch1 = am.fit(update_freq=5, disp = "off")
## ARCH(4)
am = arch_model(y, mean = 'Zero', vol='Garch', p=4, o=0, q=0, dist='Normal')
arch4 = am.fit(update_freq=5, disp = "off")
## GARCH(4,1)
am = arch_model(y, mean = 'Zero', vol='Garch', p=4, o=0, q=1, dist='Normal')
garch4_1 = am.fit(update_freq=5, disp = "off")
## GARCH(1,1)
am = arch_model(y, mean = 'Zero', vol='Garch', p=1, o=0, q=1, dist='Normal')
garch1_1 = am.fit(update_freq=5, disp = "off")
## t-GARCH(1,1)
am = arch_model(y, mean = 'Zero', vol='Garch', p=1, o=0, q=1, dist='StudentsT')
tgarch1_1 = am.fit(update_freq=5, disp = "off")
print("ARCH(1) model:", "\n", arch1.summary(), "\n")
print("ARCH(4) model:", "\n", arch4.summary(), "\n")
print("GARCH(4,1) model:", "\n", garch4_1.summary(), "\n")
print("GARCH(1,1) model:", "\n", garch1_1.summary(), "\n")
print("tGARCH(1,1) model:", "\n", tgarch1_1.summary(), "\n")


Listing 2.3/2.4: Advanced ARCH and GARCH estimation in MATLAB Last updated August 2016

aparch(y,1,1,1);     % APARCH(1,1)
aparch(y,2,2,1);     % APARCH(2,1)
aparch(y,1,1,1,'STUDENTST'); % t-APARCH(1,1)

Listing 2.3/2.4: Advanced ARCH and GARCH estimation in Python Last updated July 2020

## Leverage effects
am = arch_model(y, mean = 'Zero', vol='Garch', p=1, o=1, q=1, dist='Normal')
leverage_garch1_1 = am.fit(update_freq=5, disp = "off")
## Power models, delta = 1
am = arch_model(y, mean = 'Zero', vol='Garch', p=1, o=0, q=1, dist='Normal', power = 1.0)
power_garch1_1 = am.fit(update_freq=5, disp = "off")
print("Leverage effects:", "\n", leverage_garch1_1.summary(), "\n")
print("Power model:", "\n", power_garch1_1.summary(), "\n")