#!/usr/bin/env python3
"``naginterface.library.tsa.uni_garch_asym1`` Python Example."
# NAG Copyright 2017-2019.
# pylint: disable=invalid-name,too-many-locals
from naginterfaces.library import tsa
[docs]def main():
"""
Example for :func:`naginterfaces.library.tsa.uni_garch_asym1`.
Type-I AGARCH parameter estimation and forecasting.
>>> main()
naginterfaces.library.tsa.uni_garch_asym1 Python Example Results.
Fit a GARCH(1,1) model with Student's t-distributed residuals.
Parameter Standard
estimates errors
alpha_0 0.00 0.06
alpha_1 0.11 0.13
beta_1 0.66 0.23
gamma -0.62 0.62
df 6.25 4.70
b_0 3.85 24.11
b_1 1.48 1.82
b_2 2.15 10.16
Volatility forecast = 0.09
"""
print('naginterfaces.library.tsa.uni_garch_asym1 Python Example Results.')
print('Fit a GARCH(1,1) model with Student\'s t-distributed residuals.')
# The observations and the exogenous vectors:
yt, x = get_data()
# The details of the model to fit:
dist = 'T'
ip = 1
iq = 1
isym = 1
# Include the mean term
mn = 1
# The control parameters:
copts = [True, True]
maxit = 200
tol = 0.00001
# The initial parameter estimates for theta:
theta = [
0.05, # alpha_0
0.10, # alpha_1
0.15, # beta_1
-0.10, # gamma
2.60, # df
1.50, # b_0
0., # b_1, not required
0., # b_2, not required
]
# Pre-observed conditional variance not required:
hp = 0.
g_estim = tsa.uni_garch_asym1_estim(
dist, yt, x, ip, iq, mn, isym, theta, hp, copts, maxit, tol,
)
# The forecast horizon:
nt = 4
fht = tsa.uni_garch_asym1_forecast(
nt, ip, iq, g_estim.theta[:iq+ip+1],
g_estim.theta[iq+ip+1], g_estim.ht, g_estim.et,
)
print(' Parameter Standard')
print(' estimates errors')
for i in range(iq+1):
print(
'alpha_{:d} {:16.2f}{:16.2f}'.format(
i, g_estim.theta[i], g_estim.se[i]
)
)
for i in range(ip):
print(
' beta_{:d} {:16.2f}{:16.2f}'.format(
i+1, g_estim.theta[iq+1+i], g_estim.se[iq+1+i]
)
)
print(
' gamma {:16.2f}{:16.2f}'.format(
g_estim.theta[iq+ip+1], g_estim.se[iq+ip+1]
)
)
print(
' df {:16.2f}{:16.2f}'.format(
g_estim.theta[iq+ip+2], g_estim.se[iq+ip+2]
)
)
for i in range(len(x[0])+1):
print(
' b_{:d} {:16.2f}{:16.2f}'.format(
i, g_estim.theta[iq+ip+3+i], g_estim.se[iq+ip+3+i]
)
)
print('Volatility forecast = {:12.2f}'.format(fht[-1]))
def get_data():
"""
The observations and the exogenous vectors.
"""
# The observations:
yt = [
9.04, 9.49, 9.12, 9.23, 9.35,
9.09, 9.75, 9.23, 8.76, 9.17,
9.20, 9.64, 8.74, 9.23, 9.42,
9.70, 9.55, 10.00, 9.18, 9.77,
9.80, 9.56, 9.28, 9.68, 9.51,
9.51, 8.97, 9.30, 9.52, 9.41,
9.53, 9.75, 9.72, 9.38, 9.28,
9.42, 9.74, 9.75, 9.60, 9.90,
9.06, 9.92, 9.21, 9.57, 9.42,
8.65, 8.85, 9.61, 10.77, 10.19,
10.47, 10.10, 10.21, 9.96, 9.66,
9.79, 10.30, 9.68, 10.08, 10.38,
9.69, 9.02, 9.89, 10.46, 10.47,
9.99, 9.76, 9.78, 9.62, 10.43,
10.42, 9.95, 9.95, 9.70, 10.24,
9.78, 9.98, 8.73, 10.23, 9.10,
10.27, 9.85, 10.44, 10.30, 10.08,
10.20, 10.14, 9.89, 9.90, 11.33,
9.71, 9.40, 9.97, 10.92, 9.76,
10.16, 10.43, 9.60, 10.29, 10.03,
]
# The exogenous vectors:
x = [
[0.12, 2.40],
[0.12, 2.40],
[0.13, 2.40],
[0.14, 2.40],
[0.14, 2.40],
[0.15, 2.40],
[0.16, 2.40],
[0.16, 2.40],
[0.17, 2.40],
[0.18, 2.41],
[0.19, 2.41],
[0.19, 2.41],
[0.20, 2.41],
[0.21, 2.41],
[0.21, 2.41],
[0.22, 2.41],
[0.23, 2.41],
[0.23, 2.41],
[0.24, 2.41],
[0.25, 2.42],
[0.25, 2.42],
[0.26, 2.42],
[0.26, 2.42],
[0.27, 2.42],
[0.28, 2.42],
[0.28, 2.42],
[0.29, 2.42],
[0.30, 2.42],
[0.30, 2.42],
[0.31, 2.43],
[0.32, 2.43],
[0.32, 2.43],
[0.33, 2.43],
[0.33, 2.43],
[0.34, 2.43],
[0.35, 2.43],
[0.35, 2.43],
[0.36, 2.43],
[0.37, 2.43],
[0.37, 2.44],
[0.38, 2.44],
[0.38, 2.44],
[0.39, 2.44],
[0.39, 2.44],
[0.40, 2.44],
[0.41, 2.44],
[0.41, 2.44],
[0.42, 2.44],
[0.42, 2.44],
[0.43, 2.45],
[0.43, 2.45],
[0.44, 2.45],
[0.45, 2.45],
[0.45, 2.45],
[0.46, 2.45],
[0.46, 2.45],
[0.47, 2.45],
[0.47, 2.45],
[0.48, 2.45],
[0.48, 2.46],
[0.49, 2.46],
[0.49, 2.46],
[0.50, 2.46],
[0.50, 2.46],
[0.51, 2.46],
[0.51, 2.46],
[0.52, 2.46],
[0.52, 2.46],
[0.53, 2.46],
[0.53, 2.47],
[0.54, 2.47],
[0.54, 2.47],
[0.54, 2.47],
[0.55, 2.47],
[0.55, 2.47],
[0.56, 2.47],
[0.56, 2.47],
[0.57, 2.47],
[0.57, 2.47],
[0.57, 2.48],
[0.58, 2.48],
[0.58, 2.48],
[0.59, 2.48],
[0.59, 2.48],
[0.59, 2.48],
[0.60, 2.48],
[0.60, 2.48],
[0.61, 2.48],
[0.61, 2.48],
[0.61, 2.49],
[0.62, 2.49],
[0.62, 2.49],
[0.62, 2.49],
[0.63, 2.49],
[0.63, 2.49],
[0.63, 2.49],
[0.64, 2.49],
[0.64, 2.49],
[0.64, 2.49],
[0.64, 2.50],
]
return yt, x
if __name__ == '__main__':
import doctest
import sys
sys.exit(
doctest.testmod(
None, verbose=True, report=False,
optionflags=doctest.REPORT_NDIFF,
).failed
)
