E7_volatitlity

In [15]:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from arch import arch_model
from statsmodels.stats.diagnostic import het_arch

In [2]:

data = pd.read_csv('SSEC_daily.csv', encoding='GB2312', usecols=[2, 6])
data

Out[2]:

	交易日期	收盘
0	1997/1/2	919.44
1	1997/1/3	899.61
2	1997/1/6	876.50
3	1997/1/7	898.17
4	1997/1/8	896.41
...	...	...
5086	2017/12/29	3307.17
5087	2018/1/2	3348.33
5088	2018/1/3	3369.11
5089	2018/1/4	3385.71
5090	2018/1/5	3391.75

5091 rows × 2 columns

In [4]:

data.columns = ['date', 'close']
p = data.loc[:, ['close']].values
r = np.log(p[1:]) - np.log(p[:-1])
plt.plot(r)

Out[4]:

[<matplotlib.lines.Line2D at 0x2055742b400>]

In [5]:

# mu常数，波动率 GARCH(1, 1)，分布 正态
am_garch = arch_model(r, mean='constant', vol='garch', p=1, q=1, dist='normal') 
res_garch = am_garch.fit()
print(res_garch.summary())

Iteration:      1,   Func. Count:      6,   Neg. LLF: 1430893525100.7856
Iteration:      2,   Func. Count:     18,   Neg. LLF: -14474.835667164152
Optimization terminated successfully    (Exit mode 0)
            Current function value: -14474.835659373894
            Iterations: 6
            Function evaluations: 18
            Gradient evaluations: 2
                     Constant Mean - GARCH Model Results                      
==============================================================================
Dep. Variable:                      y   R-squared:                       0.000
Mean Model:             Constant Mean   Adj. R-squared:                  0.000
Vol Model:                      GARCH   Log-Likelihood:                14474.8
Distribution:                  Normal   AIC:                          -28941.7
Method:            Maximum Likelihood   BIC:                          -28915.5
                                        No. Observations:                 5090
Date:                Thu, May 25 2023   Df Residuals:                     5089
Time:                        18:21:52   Df Model:                            1
                                 Mean Model                                 
============================================================================
                 coef    std err          t      P>|t|      95.0% Conf. Int.
----------------------------------------------------------------------------
mu         2.2201e-04  2.409e-05      9.215  3.125e-20 [1.748e-04,2.692e-04]
                              Volatility Model                              
============================================================================
                 coef    std err          t      P>|t|      95.0% Conf. Int.
----------------------------------------------------------------------------
omega      5.2878e-06  1.591e-12  3.323e+06      0.000 [5.288e-06,5.288e-06]
alpha[1]       0.1000  1.077e-02      9.283  1.653e-20   [7.889e-02,  0.121]
beta[1]        0.8800  9.380e-03     93.813      0.000     [  0.862,  0.898]
============================================================================

Covariance estimator: robust

C:\ProgramData\Anaconda3\lib\site-packages\arch\univariate\base.py:310: DataScaleWarning: y is poorly scaled, which may affect convergence of the optimizer when
estimating the model parameters. The scale of y is 0.0002644. Parameter
estimation work better when this value is between 1 and 1000. The recommended
rescaling is 100 * y.

This warning can be disabled by either rescaling y before initializing the
model or by setting rescale=False.

  warnings.warn(

In [7]:

# mu AR，波动率 GARCH(1, 1)，分布 正态
am_ar_garch = arch_model(r, mean='ar', lags=1, vol='garch', p=1, q=1, dist='normal')
res_am_ar_garch = am_ar_garch.fit()
print(res_am_ar_garch.summary())

Iteration:      1,   Func. Count:      7,   Neg. LLF: 887808619677.113
Iteration:      2,   Func. Count:     20,   Neg. LLF: -14472.862358762366
Optimization terminated successfully    (Exit mode 0)
            Current function value: -14472.86235098874
            Iterations: 6
            Function evaluations: 20
            Gradient evaluations: 2
                           AR - GARCH Model Results                           
==============================================================================
Dep. Variable:                      y   R-squared:                       0.000
Mean Model:                        AR   Adj. R-squared:                 -0.000
Vol Model:                      GARCH   Log-Likelihood:                14472.9
Distribution:                  Normal   AIC:                          -28935.7
Method:            Maximum Likelihood   BIC:                          -28903.1
                                        No. Observations:                 5089
Date:                Thu, May 25 2023   Df Residuals:                     5087
Time:                        18:31:10   Df Model:                            2
                                  Mean Model                                 
=============================================================================
                 coef    std err          t      P>|t|       95.0% Conf. Int.
-----------------------------------------------------------------------------
Const      2.1909e-04  4.828e-05      4.538  5.683e-06  [1.245e-04,3.137e-04]
y[1]           0.0114  1.581e-02      0.720      0.472 [-1.961e-02,4.238e-02]
                              Volatility Model                              
============================================================================
                 coef    std err          t      P>|t|      95.0% Conf. Int.
----------------------------------------------------------------------------
omega      5.2862e-06  6.250e-11  8.458e+04      0.000 [5.286e-06,5.286e-06]
alpha[1]       0.1000  1.108e-02      9.024  1.817e-19   [7.828e-02,  0.122]
beta[1]        0.8800  9.690e-03     90.812      0.000     [  0.861,  0.899]
============================================================================

Covariance estimator: robust

C:\ProgramData\Anaconda3\lib\site-packages\arch\univariate\base.py:310: DataScaleWarning: y is poorly scaled, which may affect convergence of the optimizer when
estimating the model parameters. The scale of y is 0.0002643. Parameter
estimation work better when this value is between 1 and 1000. The recommended
rescaling is 100 * y.

This warning can be disabled by either rescaling y before initializing the
model or by setting rescale=False.

  warnings.warn(

In [11]:

sim_garch = arch_model(None, mean='constant', vol='garch', dist='normal', p=1, q=1)
# print(res_garch.params)
# sim_paras = res_garch.params
sim_paras = pd.Series([0.0006, 0.00008, 0.15, 0.8], index=['mu', 'omega', 'alpha[1]', 'beta[1]'])
sim_garch_data = sim_garch.simulate(sim_paras, 1000)
plt.plot(sim_garch_data)

Out[11]:

[<matplotlib.lines.Line2D at 0x20559042460>,
 <matplotlib.lines.Line2D at 0x20559042520>,
 <matplotlib.lines.Line2D at 0x205590425e0>]

In [13]:

am_egarch = arch_model(r*100, mean='constant', vol='egarch', p=1, q=1, o=1)
res_egarch = am_egarch.fit()
print(res_egarch.summary())

Iteration:      1,   Func. Count:      7,   Neg. LLF: 41310.24007067039
Iteration:      2,   Func. Count:     20,   Neg. LLF: 41311.930866633185
Iteration:      3,   Func. Count:     31,   Neg. LLF: 1053056504.8062321
Iteration:      4,   Func. Count:     41,   Neg. LLF: 9326.272080588187
Iteration:      5,   Func. Count:     49,   Neg. LLF: 69534.02742630933
Iteration:      6,   Func. Count:     57,   Neg. LLF: 8932.101523765676
Iteration:      7,   Func. Count:     64,   Neg. LLF: 9020.736319561376
Iteration:      8,   Func. Count:     72,   Neg. LLF: 8930.874073790517
Iteration:      9,   Func. Count:     79,   Neg. LLF: 8907.632705122136
Iteration:     10,   Func. Count:     85,   Neg. LLF: 8907.626055527973
Iteration:     11,   Func. Count:     91,   Neg. LLF: 8907.625999106054
Iteration:     12,   Func. Count:     97,   Neg. LLF: 8907.626001698038
Iteration:     13,   Func. Count:    104,   Neg. LLF: 8907.625987108073
Iteration:     14,   Func. Count:    109,   Neg. LLF: 8907.625987105723
Optimization terminated successfully    (Exit mode 0)
            Current function value: 8907.625987108073
            Iterations: 14
            Function evaluations: 109
            Gradient evaluations: 14
                     Constant Mean - EGARCH Model Results                     
==============================================================================
Dep. Variable:                      y   R-squared:                       0.000
Mean Model:             Constant Mean   Adj. R-squared:                  0.000
Vol Model:                     EGARCH   Log-Likelihood:               -8907.63
Distribution:                  Normal   AIC:                           17825.3
Method:            Maximum Likelihood   BIC:                           17857.9
                                        No. Observations:                 5090
Date:                Thu, May 25 2023   Df Residuals:                     5089
Time:                        18:46:27   Df Model:                            1
                                 Mean Model                                 
============================================================================
                 coef    std err          t      P>|t|      95.0% Conf. Int.
----------------------------------------------------------------------------
mu             0.0145  3.658e-03      3.969  7.232e-05 [7.347e-03,2.169e-02]
                               Volatility Model                               
==============================================================================
                 coef    std err          t      P>|t|        95.0% Conf. Int.
------------------------------------------------------------------------------
omega          0.0181  4.295e-03      4.219  2.451e-05   [9.703e-03,2.654e-02]
alpha[1]       0.1737  2.338e-02      7.431  1.080e-13       [  0.128,  0.220]
gamma[1]      -0.0232  9.989e-03     -2.326  2.002e-02 [-4.281e-02,-3.657e-03]
beta[1]        0.9886  3.916e-03    252.442      0.000       [  0.981,  0.996]
==============================================================================

Covariance estimator: robust

In [20]:

result_arch_test = het_arch(r, nlags=10)
print(result_arch_test)

(452.0287706945414, 7.713522349298394e-91, 49.51054630896014, 2.8996625106266254e-95)

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