CS计算机代考程序代写 python Excel ARCH_share

ARCH_share

July 22, 2021

Importing packages

[61]: #importing packages
import statsmodels.api as sm
from statsmodels.tsa.stattools import adfuller
import pandas as pd
import numpy as np
import statsmodels.formula.api as smf
from sklearn import linear_model
import matplotlib.pyplot as plt

Reading Excel file saved in hard drive

[62]: #reading the file
df = pd.read_excel(“C:\\Users\\rluck\\OneDrive\\share.xlsx”)
df

[62]: OBS PRICE
0 1 975.04
1 2 977.07
2 3 966.58
3 4 964.00
4 5 956.05
.. … …
989 990 1144.80
990 991 1170.35
991 992 1167.10
992 993 1158.31
993 994 1139.93

[994 rows x 2 columns]

Calculating daily returns and daily squared returns from SP500

Daily returns (R)
R = 100 ∗ ln(Pt/Pt−1)

Daily squared returns (R2)
R = R2

[63]: #computing the inflation rate
df[‘R’] = 100*np.log(df[‘PRICE’]/df[‘PRICE’].shift(1))
df[‘R_squared’] = df[‘R’]**2
df = df.dropna(subset=[“R”])
df

[63]: OBS PRICE R R_squared
1 2 977.07 0.207980 0.043256
2 3 966.58 -1.079423 1.165154
3 4 964.00 -0.267277 0.071437
4 5 956.05 -0.828108 0.685763
5 6 927.69 -3.011259 9.067679
.. … … … …
989 990 1144.80 1.310082 1.716314
990 991 1170.35 2.207290 4.872129
991 992 1167.10 -0.278081 0.077329
992 993 1158.31 -0.755999 0.571535
993 994 1139.93 -1.599519 2.558461

[993 rows x 4 columns]

$Plotting the time series: R and R2$

[64]: #plotting the R series
plt.plot(df[‘R’],label=’R’)
plt.legend(loc=’best’, fontsize=’large’)
plt.show()

[65]: #plotting the R_squared series
plt.plot(df[‘R_squared’],label=’R_squared’,color=’Red’)
plt.legend(loc=’best’, fontsize=’large’)
plt.show()

Histogram and descriptive statistics

[66]: #Plot histogram of R
plt.hist(df[‘R’],bins=120,label=’R’, density=True, alpha=0.6, color=’b’)
plt.legend(loc=’best’, fontsize=’large’)
plt.show()

[67]: from scipy import stats
stats.describe(df[‘R’])

[67]: DescribeResult(nobs=993, minmax=(-7.043759037302043, 4.964596183505854),
mean=0.01573450555862576, variance=1.694877827267905,
skewness=-0.1468232170367387, kurtosis=2.016094075647234)

[68]: stats.jarque_bera(df[‘R’])

[68]: Jarque_beraResult(statistic=171.7419793855507, pvalue=0.0)

[69]: #Plot histogram of R_squared
plt.hist(df[‘R_squared’],bins=120,label=’R_squared’, density=True, alpha=0.6,␣
↪→color=’b’)

plt.legend(loc=’best’, fontsize=’large’)
plt.show()

[70]: stats.describe(df[‘R_squared’])

[70]: DescribeResult(nobs=993, minmax=(0.0, 49.614541375574206),
mean=1.693418576326566, variance=11.506356201573688, skewness=6.16939777089506,
kurtosis=59.64692480452559)

[71]: stats.jarque_bera(df[‘R_squared’])

[71]: Jarque_beraResult(statistic=153501.31264418407, pvalue=0.0)

ACF , PACF of R

[72]: from statsmodels.graphics import tsaplots
fig =tsaplots.plot_acf(df[‘R’],lags=16)
fig =tsaplots.plot_pacf(df[‘R’],lags=16)
plt.show()

[73]: # Generating the Q tables
import numpy as np
r,q,p = sm.tsa.acf(df[‘R’].values.squeeze(), qstat=True)
data = np.c_[range(1,41), r[1:], q, p]
table = pd.DataFrame(data, columns=[‘lag’, “AC”, “Q”, “Prob(>Q)”])
print (table.set_index(‘lag’))

AC Q Prob(>Q)
lag
1.0 0.002187 0.004765 0.944967
2.0 -0.044549 1.983469 0.370933
3.0 -0.042759 3.808159 0.282939
4.0 0.036575 5.144571 0.272783
5.0 -0.068961 9.900359 0.078108
6.0 -0.019748 10.290740 0.112930
7.0 -0.001411 10.292735 0.172582
8.0 -0.019274 10.665353 0.221391
9.0 -0.019877 11.062067 0.271479
10.0 0.014334 11.268578 0.336980
11.0 -0.054077 14.210889 0.221543
12.0 0.077208 20.214671 0.063133
13.0 0.059358 23.766889 0.033343
14.0 -0.008254 23.835639 0.047960
15.0 0.039619 25.421426 0.044562
16.0 -0.040201 27.055817 0.040867
17.0 0.014268 27.261915 0.054337
18.0 -0.057071 30.562506 0.032324
19.0 0.021465 31.029898 0.040069
20.0 -0.010472 31.141257 0.053353
21.0 -0.054597 34.171259 0.034738
22.0 -0.015008 34.400460 0.044705
23.0 0.028022 35.200283 0.049681
24.0 0.036951 36.592496 0.048029
25.0 -0.033563 37.742296 0.049009
26.0 0.017079 38.040350 0.060041
27.0 0.082436 44.991090 0.016296
28.0 0.001189 44.992538 0.022101
29.0 0.017297 45.299169 0.027513
30.0 -0.000220 45.299219 0.036196
31.0 0.004336 45.318524 0.046688
32.0 -0.053556 48.267405 0.032500
33.0 -0.040998 49.997358 0.029234
34.0 -0.089707 58.288305 0.005893
35.0 -0.037434 59.733514 0.005697
36.0 0.025398 60.399493 0.006620
37.0 -0.010012 60.503099 0.008705
38.0 -0.001130 60.504421 0.011575
39.0 0.057283 63.902786 0.007182

40.0 -0.073371 69.484020 0.002633

C:\Users\rluck\anaconda3\lib\site-packages\statsmodels\tsa\stattools.py:657:
FutureWarning: The default number of lags is changing from 40 tomin(int(10 *
np.log10(nobs)), nobs – 1) after 0.12is released. Set the number of lags to an
integer to silence this warning.

warnings.warn(
C:\Users\rluck\anaconda3\lib\site-packages\statsmodels\tsa\stattools.py:667:
FutureWarning: fft=True will become the default after the release of the 0.12
release of statsmodels. To suppress this warning, explicitly set fft=False.

warnings.warn(

$ACF , PACF of R2$

[74]: fig =tsaplots.plot_acf(df[‘R_squared’],lags=16)
fig =tsaplots.plot_pacf(df[‘R_squared’],lags=16)
plt.show()

[75]: # Generating the Q tables
import numpy as np
r,q,p = sm.tsa.acf(df[‘R_squared’].values.squeeze(), qstat=True)
data = np.c_[range(1,41), r[1:], q, p]
table = pd.DataFrame(data, columns=[‘lag’, “AC”, “Q”, “Prob(>Q)”])
print (table.set_index(‘lag’))

AC Q Prob(>Q)
lag
1.0 0.116401 13.495026 2.391966e-04
2.0 0.137366 32.307886 9.647874e-08
3.0 0.045022 34.330823 1.686854e-07
4.0 0.043314 36.205092 2.625763e-07
5.0 0.163064 62.795866 3.208813e-12
6.0 0.055033 65.827678 2.922824e-12
7.0 0.088429 73.663464 2.678057e-13
8.0 0.072519 78.938732 7.992968e-14
9.0 0.026248 79.630526 1.913609e-13
10.0 0.051198 82.265203 1.803486e-13
11.0 0.065028 86.519895 7.988149e-14
12.0 0.041676 88.269223 1.067025e-13
13.0 -0.014482 88.480668 2.726470e-13
14.0 0.010197 88.585610 7.015944e-13
15.0 0.001769 88.588769 1.817136e-12
16.0 0.091960 97.140862 1.186384e-13

17.0 0.036990 98.525997 1.667347e-13
18.0 0.072813 103.898575 4.253523e-14
19.0 0.076362 109.813725 8.627403e-15
20.0 0.020351 110.234269 1.780030e-14
21.0 0.110912 122.738581 2.240937e-16
22.0 0.050038 125.286355 1.894182e-16
23.0 -0.001192 125.287803 4.611835e-16
24.0 0.044396 127.297499 4.775153e-16
25.0 0.003592 127.310670 1.115576e-15
26.0 0.028843 128.160663 1.814862e-15
27.0 0.082465 135.116334 2.425735e-16
28.0 0.026399 135.829855 4.136894e-16
29.0 -0.004892 135.854381 9.184485e-16
30.0 -0.007907 135.918535 1.972095e-15
31.0 0.009156 136.004633 4.128389e-15
32.0 0.079173 142.449347 6.937586e-16
33.0 0.006087 142.487482 1.465969e-15
34.0 -0.039022 144.056309 1.678684e-15
35.0 -0.018729 144.418079 3.052000e-15
36.0 -0.038257 145.929177 3.521024e-15
37.0 -0.025003 146.575300 5.624595e-15
38.0 -0.043604 148.542369 5.383179e-15
39.0 -0.014147 148.749640 9.993128e-15
40.0 -0.042500 150.622304 9.812920e-15

warnings.warn(

ARCH(5)

[76]: from arch import arch_model

[77]: dt = df[‘R’]
model = arch_model(dt,mean =’Constant’, vol =’ARCH’, q=5)
x_5 =model.fit(update_freq=0)
x_5

Optimization terminated successfully (Exit mode 0)
Current function value: 1664.047869085027
Iterations: 5
Function evaluations: 28
Gradient evaluations: 5

[77]: Constant Mean – ARCH Model Results
==============================================================================
Dep. Variable: R R-squared: 0.000
Mean Model: Constant Mean Adj. R-squared: 0.000
Vol Model: ARCH Log-Likelihood: -1664.05
Distribution: Normal AIC: 3334.10
Method: Maximum Likelihood BIC: 3348.80

No. Observations: 993
Date: Thu, Jul 22 2021 Df Residuals: 992
Time: 20:04:12 Df Model: 1

Mean Model
===========================================================================

coef std err t P>|t| 95.0% Conf. Int.
—————————————————————————
mu 0.0293 4.132e-02 0.709 0.478 [-5.170e-02, 0.110]

Volatility Model
===========================================================================

coef std err t P>|t| 95.0% Conf. Int.
—————————————————————————
omega 1.5288 0.104 14.654 1.263e-48 [ 1.324, 1.733]
alpha[1] 0.0963 4.954e-02 1.944 5.194e-02 [-8.088e-04, 0.193]
===========================================================================

Covariance estimator: robust
ARCHModelResult, id: 0x21914bdbe20

[78]: #Aligning AIC, BIC from Python with Stata’s AIC, BIC
n =993
name = [‘AIC_stata’,’BIC_stata’]
stata=[x_5.aic/n,x_5.bic/n]
lzip(name, stata)

[78]: [(‘AIC_stata’, 3.357598930684848), (‘BIC_stata’, 3.3724047635067365)]

ARCH Test

[79]: from statsmodels.stats.diagnostic import het_arch
from statsmodels.compat import lzip
res = het_arch(dt.values, nlags=5)
name =[‘lm’,’lm_pval’,’fval’,’f_pval’]
lzip(name,res)

[79]: [(‘lm’, 52.586810853630816),
(‘lm_pval’, 4.0887029149590036e-10),
(‘fval’, 11.041163168843253),
(‘f_pval’, 2.3131694315533897e-10)]

ARCH Test of Standardised Residuals

[80]: std_resid = x_5.resid/x_5.conditional_volatility
res = het_arch(std_resid, nlags=5)
name =[‘lm’,’lm_pval’,’fval’,’f_pval’]
lzip(name,res)

[80]: [(‘lm’, 44.61654794255047),
(‘lm_pval’, 1.7360584950680533e-08),
(‘fval’, 9.2885771918154),
(‘f_pval’, 1.1768118600559285e-08)]

Histogram of Residuals

[81]: #Historgram of residuals
resid = x_5.resid
plt.hist(resid,bins=120,label=’Resid’, density=True, alpha=0.6, color=’b’)
plt.legend(loc=’best’, fontsize=’large’)
plt.show()

[82]: stats.describe(resid)

[82]: DescribeResult(nobs=993, minmax=(-7.073049296466991, 4.9353059243409065),
mean=-0.013555753606322416, variance=1.694877827267905,
skewness=-0.1468232170367387, kurtosis=2.016094075647234)

[83]: stats.jarque_bera(resid)

[83]: Jarque_beraResult(statistic=171.7419793855507, pvalue=0.0)

ACF , PACF of Squared Residuals

[84]: fig =tsaplots.plot_acf(resid**2,lags=16)
fig =tsaplots.plot_pacf(resid**2,lags=16)
plt.show()

Histogram of Standardised Residuals

[85]: #Historgram of std residuals
plt.hist(std_resid,bins=120,label=’Std_Resid’, density=True, alpha=0.6,␣
↪→color=’b’)

plt.legend(loc=’best’, fontsize=’large’)
plt.show()

[86]: stats.describe(std_resid)

[86]: DescribeResult(nobs=993, minmax=(-5.343797790419605, 3.8965888804733484),
mean=-0.014086543542439298, variance=1.0008098057706427,
skewness=-0.17614610401990488, kurtosis=1.8124982770599578)

[87]: stats.jarque_bera(std_resid)

[87]: Jarque_beraResult(statistic=141.05812439839767, pvalue=0.0)

ACF , PACF of Squared Std Residuals

[88]: fig =tsaplots.plot_acf(std_resid**2,lags=16)
fig =tsaplots.plot_pacf(std_resid**2,lags=16)
plt.show()

Choosing the ARCH lags

[89]: #Running ARCH from p=1 to p =9
model_1 = arch_model(dt,mean =’Constant’, vol =’ARCH’, p=1)
model_2 = arch_model(dt,mean =’Constant’, vol =’ARCH’, p=2)
model_3 = arch_model(dt,mean =’Constant’, vol =’ARCH’, p=3)
model_4 = arch_model(dt,mean =’Constant’, vol =’ARCH’, p=4)
model_5 = arch_model(dt,mean =’Constant’, vol =’ARCH’, p=5)
model_6 = arch_model(dt,mean =’Constant’, vol =’ARCH’, p=6)
model_7 = arch_model(dt,mean =’Constant’, vol =’ARCH’, p=7)
model_8 = arch_model(dt,mean =’Constant’, vol =’ARCH’, p=8)
model_9 = arch_model(dt,mean =’Constant’, vol =’ARCH’, p=9)
x_1= model_1.fit(update_freq=0)
x_2= model_2.fit(update_freq=0)
x_3= model_3.fit(update_freq=0)
x_4= model_4.fit(update_freq=0)
x_5= model_5.fit(update_freq=0)
x_6= model_6.fit(update_freq=0)
x_7= model_7.fit(update_freq=0)
x_8= model_8.fit(update_freq=0)
x_9= model_9.fit(update_freq=0)

Optimization terminated successfully (Exit mode 0)
Current function value: 1664.047869085027
Iterations: 5
Function evaluations: 28
Gradient evaluations: 5

Optimization terminated successfully (Exit mode 0)
Current function value: 1651.3667967409056
Iterations: 8
Function evaluations: 49
Gradient evaluations: 8

Optimization terminated successfully (Exit mode 0)
Current function value: 1650.803109203952
Iterations: 12
Function evaluations: 83
Gradient evaluations: 12

Optimization terminated successfully (Exit mode 0)
Current function value: 1645.3224422301862
Iterations: 13
Function evaluations: 104
Gradient evaluations: 13

Optimization terminated successfully (Exit mode 0)
Current function value: 1639.433689366865
Iterations: 15
Function evaluations: 135
Gradient evaluations: 15

Optimization terminated successfully (Exit mode 0)
Current function value: 1638.5159772755142
Iterations: 15

Function evaluations: 153
Gradient evaluations: 15

Optimization terminated successfully (Exit mode 0)
Current function value: 1635.51431460451
Iterations: 15
Function evaluations: 170
Gradient evaluations: 15

Optimization terminated successfully (Exit mode 0)
Current function value: 1631.19776764798
Iterations: 17
Function evaluations: 209
Gradient evaluations: 17

Optimization terminated successfully (Exit mode 0)
Current function value: 1631.1128849200488
Iterations: 20
Function evaluations: 264
Gradient evaluations: 20

[90]: #Computing the AIC (AIC_stata= AIC_Python/ no of obs)
n = 993
aic=[x_1.aic/n,x_2.aic/n,x_3.aic/n,x_4.aic/n,x_5.aic/n,x_6.aic/n,x_7.aic/n,x_8.
↪→aic/n,x_9.aic/n]

bic= [x_1.bic/n,x_2.bic/n,x_3.bic/n,x_4.bic/n,x_5.bic/n,x_6.bic/n,x_7.bic/n,x_8.
↪→bic/n,x_9.bic/n]

name␣
↪→=[‘ARCH_1′,’ARCH_2′,’ARCH_3′,’ARCH_4′,’ARCH_5′,’ARCH_6′,’ARCH_7′,’ARCH_8′,’ARCH_9’]

lzip(name,aic, bic)

[90]: [(‘ARCH_1’, 3.357598930684848, 3.3724047635067365),
(‘ARCH_2’, 3.334072098168994, 3.3538132085981793),
(‘ARCH_3’, 3.3349508745296115, 3.359627262566093),
(‘ARCH_4’, 3.325926369043678, 3.3555380346874557),
(‘ARCH_5’, 3.316079938301843, 3.350626881552917),
(‘ARCH_6’, 3.3162456742709248, 3.3557278951292946),
(‘ARCH_7’, 3.31221412810576, 3.3566316265714264),
(‘ARCH_8’, 3.305534275222518, 3.35488705129548),
(‘ARCH_9′, 3.3073774117221526, 3.361665465402411)]

[91]: #Defining Conditional_Variance as squared conditional volatility from ARCH(5)␣
↪→which was defined as x_5 beforehand

conditional_variance = x_5.conditional_volatility**2

[92]: #Plotting the R and Conditional Variance from ARCH(5)
dt.plot(figsize=(12,5), color =’red’,label =’R’)
conditional_variance.plot(figsize=(12,5),color=’blue’,label=’cond_variance’)
plt.title(‘ARCH (5) Conditional Variance’, size=15)
plt.legend(loc=’best’, fontsize=’large’)

plt.show()

[ ]:

Related Posts