In [1]: import pandas as pd
import pandas_datareader.data as reader
import statsmodels.api as sm
from scipy.stats import f
import matplotlib.pyplot as plt
import numpy as np
Defining data frame
In [2]: df = pd.read_excel('Test Portfolios.xlsx')
Defining Variables
In [3]: # defining dependent variables for 7 factors (a) - SORTING ISLAMIC PORTFOLIOS BASED ON
dependent_vars7b = ['SL', 'SN1', 'SH', 'BL', 'BN1', 'BH', 'SW', 'SN2', 'SR', 'BW', 'BN
# defining independent variables for 7 factors (a) - ADJUSTING SMBI AND IMTI FACTORS
independent_vars7b = ['Rm-Rf', 'SMBP', 'HML', 'RMW', 'CMA', 'PMU', 'IMTP']
In [4]: # Add a constant to the independent variables
X7b = sm.add_constant(df[independent_vars7b])
Run the regression
In [7]: for dv in dependent_vars7b:
model = sm.OLS(df[dv], X7b)
results = model.fit(cov_type = 'HAC', cov_kwds = {'maxlags': 1}) # cov_type='HAC',
print(f'Regression results for {dv}:')
print(results.summary())
print('\n---\n')
Regression results for SL:
OLS Regression Results
==============================================================================
Dep. Variable:
SL
R-squared:
0.890
Model:
OLS
Adj. R-squared:
0.884
Method:
Least Squares
F-statistic:
124.1
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
7.51e-56
Time:
14:44:09
Log-Likelihood:
302.79
No. Observations:
144
AIC:
-589.6
Df Residuals:
136
BIC:
-565.8
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
0.0005
0.003
0.171
0.864
-0.005
0.006
Rm-Rf
1.0145
0.060
16.860
0.000
0.897
1.132
SMBP
1.0968
0.075
14.614
0.000
0.950
1.244
HML
-1.1364
0.111
-10.224
0.000
-1.354
-0.919
RMW
-0.2271
0.127
-1.790
0.074
-0.476
0.022
CMA
-0.0494
0.068
-0.731
0.465
-0.182
0.083
PMU
0.1241
0.070
1.775
0.076
-0.013
0.261
IMTP
0.0370
0.075
0.496
0.620
-0.109
0.183
==============================================================================
Omnibus:
17.501
Durbin-Watson:
2.011
Prob(Omnibus):
0.000
Jarque-Bera (JB):
34.358
Skew:
0.528
Prob(JB):
3.46e-08
Kurtosis:
5.147
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for SN1:
OLS Regression Results
==============================================================================
Dep. Variable:
SN1
R-squared:
0.873
Model:
OLS
Adj. R-squared:
0.867
Method:
Least Squares
F-statistic:
129.5
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
6.18e-57
Time:
14:44:09
Log-Likelihood:
319.46
No. Observations:
144
AIC:
-622.9
Df Residuals:
136
BIC:
-599.2
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0059
0.002
-2.521
0.012
-0.010
-0.001
Rm-Rf
0.8174
0.059
13.952
0.000
0.703
0.932
SMBP
0.8216
0.093
8.846
0.000
0.640
1.004
HML
0.0730
0.061
1.197
0.231
-0.047
0.192
RMW
-0.2111
0.076
-2.777
0.005
-0.360
-0.062
CMA
-0.1529
0.073
-2.085
0.037
-0.297
-0.009
PMU
0.2055
0.062
3.316
0.001
0.084
0.327
IMTP
-0.0751
0.065
-1.157
0.247
-0.202
0.052
==============================================================================
Omnibus:
29.485
Durbin-Watson:
1.840
Prob(Omnibus):
0.000
Jarque-Bera (JB):
52.251
Skew:
0.956
Prob(JB):
4.51e-12
Kurtosis:
5.247
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for SH:
OLS Regression Results
==============================================================================
Dep. Variable:
SH
R-squared:
0.929
Model:
OLS
Adj. R-squared:
0.925
Method:
Least Squares
F-statistic:
278.7
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
2.32e-77
Time:
14:44:09
Log-Likelihood:
353.63
No. Observations:
144
AIC:
-691.3
Df Residuals:
136
BIC:
-667.5
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
0.0031
0.002
1.810
0.070
-0.000
0.006
Rm-Rf
0.9136
0.041
22.220
0.000
0.833
0.994
SMBP
1.1167
0.054
20.572
0.000
1.010
1.223
HML
0.3832
0.054
7.110
0.000
0.278
0.489
RMW
-0.1513
0.057
-2.656
0.008
-0.263
-0.040
CMA
0.1110
0.059
1.867
0.062
-0.006
0.227
PMU
0.0412
0.037
1.105
0.269
-0.032
0.114
IMTP
0.0657
0.050
1.319
0.187
-0.032
0.163
==============================================================================
Omnibus:
6.493
Durbin-Watson:
2.078
Prob(Omnibus):
0.039
Jarque-Bera (JB):
6.093
Skew:
-0.481
Prob(JB):
0.0475
Kurtosis:
3.299
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for BL:
OLS Regression Results
==============================================================================
Dep. Variable:
BL
R-squared:
0.835
Model:
OLS
Adj. R-squared:
0.827
Method:
Least Squares
F-statistic:
104.8
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
1.33e-51
Time:
14:44:09
Log-Likelihood:
346.49
No. Observations:
144
AIC:
-677.0
Df Residuals:
136
BIC:
-653.2
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0005
0.002
-0.290
0.772
-0.004
0.003
Rm-Rf
0.8515
0.053
15.955
0.000
0.747
0.956
SMBP
0.1249
0.063
1.970
0.049
0.001
0.249
HML
-0.1469
0.043
-3.402
0.001
-0.232
-0.062
RMW
-0.0593
0.063
-0.946
0.344
-0.182
0.064
CMA
0.0053
0.063
0.085
0.932
-0.117
0.128
PMU
0.0310
0.044
0.710
0.478
-0.055
0.116
IMTP
0.0767
0.053
1.443
0.149
-0.027
0.181
==============================================================================
Omnibus:
7.160
Durbin-Watson:
2.097
Prob(Omnibus):
0.028
Jarque-Bera (JB):
12.745
Skew:
0.060
Prob(JB):
0.00171
Kurtosis:
4.452
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for BN1:
OLS Regression Results
==============================================================================
Dep. Variable:
BN1
R-squared:
0.903
Model:
OLS
Adj. R-squared:
0.898
Method:
Least Squares
F-statistic:
349.5
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
1.24e-83
Time:
14:44:09
Log-Likelihood:
368.24
No. Observations:
144
AIC:
-720.5
Df Residuals:
136
BIC:
-696.7
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0048
0.002
-3.012
0.003
-0.008
-0.002
Rm-Rf
0.9506
0.038
25.187
0.000
0.877
1.025
SMBP
-0.1951
0.066
-2.963
0.003
-0.324
-0.066
HML
-0.0265
0.056
-0.474
0.635
-0.136
0.083
RMW
-0.0763
0.054
-1.419
0.156
-0.182
0.029
CMA
0.0017
0.057
0.030
0.976
-0.110
0.113
PMU
0.0826
0.046
1.792
0.073
-0.008
0.173
IMTP
-0.0947
0.054
-1.750
0.080
-0.201
0.011
==============================================================================
Omnibus:
16.473
Durbin-Watson:
1.965
Prob(Omnibus):
0.000
Jarque-Bera (JB):
28.968
Skew:
-0.538
Prob(JB):
5.12e-07
Kurtosis:
4.916
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
---
Regression results for BH:
OLS Regression Results
==============================================================================
Dep. Variable:
BH
R-squared:
0.847
Model:
OLS
Adj. R-squared:
0.839
Method:
Least Squares
F-statistic:
74.01
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
2.86e-43
Time:
14:44:09
Log-Likelihood:
307.56
No. Observations:
144
AIC:
-599.1
Df Residuals:
136
BIC:
-575.4
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0032
0.003
-1.265
0.206
-0.008
0.002
Rm-Rf
0.9523
0.065
14.701
0.000
0.825
1.079
SMBP
0.1050
0.062
1.703
0.089
-0.016
0.226
HML
0.3335
0.086
3.874
0.000
0.165
0.502
RMW
-0.1352
0.111
-1.220
0.223
-0.353
0.082
CMA
-0.1550
0.076
-2.047
0.041
-0.303
-0.007
PMU
0.1139
0.069
1.646
0.100
-0.022
0.249
IMTP
0.0480
0.068
0.708
0.479
-0.085
0.181
==============================================================================
Omnibus:
8.553
Durbin-Watson:
2.159
Prob(Omnibus):
0.014
Jarque-Bera (JB):
12.130
Skew:
0.315
Prob(JB):
0.00232
Kurtosis:
4.275
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for SW:
OLS Regression Results
==============================================================================
Dep. Variable:
SW
R-squared:
0.910
Model:
OLS
Adj. R-squared:
0.906
Method:
Least Squares
F-statistic:
201.6
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
1.53e-68
Time:
14:44:10
Log-Likelihood:
345.59
No. Observations:
144
AIC:
-675.2
Df Residuals:
136
BIC:
-651.4
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0020
0.002
-1.122
0.262
-0.006
0.002
Rm-Rf
0.9017
0.055
16.500
0.000
0.795
1.009
SMBP
0.8785
0.068
12.936
0.000
0.745
1.012
HML
0.0237
0.053
0.448
0.654
-0.080
0.128
RMW
-0.4682
0.060
-7.835
0.000
-0.585
-0.351
CMA
0.1627
0.065
2.487
0.013
0.034
0.291
PMU
0.0541
0.046
1.188
0.235
-0.035
0.143
IMTP
-0.0933
0.050
-1.882
0.060
-0.190
0.004
==============================================================================
Omnibus:
4.008
Durbin-Watson:
1.993
Prob(Omnibus):
0.135
Jarque-Bera (JB):
4.531
Skew:
0.139
Prob(JB):
0.104
Kurtosis:
3.823
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for SN2:
OLS Regression Results
==============================================================================
Dep. Variable:
SN2
R-squared:
0.835
Model:
OLS
Adj. R-squared:
0.827
Method:
Least Squares
F-statistic:
90.30
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
5.62e-48
Time:
14:44:10
Log-Likelihood:
303.08
No. Observations:
144
AIC:
-590.2
Df Residuals:
136
BIC:
-566.4
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0038
0.003
-1.472
0.141
-0.009
0.001
Rm-Rf
0.9787
0.063
15.518
0.000
0.855
1.102
SMBP
0.9305
0.104
8.913
0.000
0.726
1.135
HML
0.1066
0.079
1.350
0.177
-0.048
0.261
RMW
-0.2092
0.093
-2.241
0.025
-0.392
-0.026
CMA
-0.3748
0.120
-3.111
0.002
-0.611
-0.139
PMU
-0.0862
0.064
-1.352
0.176
-0.211
0.039
IMTP
-0.0006
0.078
-0.008
0.993
-0.153
0.151
==============================================================================
Omnibus:
9.159
Durbin-Watson:
1.857
Prob(Omnibus):
0.010
Jarque-Bera (JB):
17.020
Skew:
-0.203
Prob(JB):
0.000201
Kurtosis:
4.635
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for SR:
OLS Regression Results
==============================================================================
Dep. Variable:
SR
R-squared:
0.867
Model:
OLS
Adj. R-squared:
0.860
Method:
Least Squares
F-statistic:
121.6
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
2.40e-55
Time:
14:44:10
Log-Likelihood:
298.59
No. Observations:
144
AIC:
-581.2
Df Residuals:
136
BIC:
-557.4
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0040
0.003
-1.552
0.121
-0.009
0.001
Rm-Rf
0.9554
0.078
12.194
0.000
0.802
1.109
SMBP
1.0073
0.097
10.366
0.000
0.817
1.198
HML
0.1088
0.086
1.271
0.204
-0.059
0.277
RMW
1.0127
0.107
9.479
0.000
0.803
1.222
CMA
0.0858
0.081
1.061
0.289
-0.073
0.244
PMU
0.2676
0.076
3.545
0.000
0.120
0.416
IMTP
-0.1068
0.074
-1.449
0.147
-0.251
0.038
==============================================================================
Omnibus:
1.769
Durbin-Watson:
2.190
Prob(Omnibus):
0.413
Jarque-Bera (JB):
1.382
Skew:
-0.086
Prob(JB):
0.501
Kurtosis:
3.448
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for BW:
OLS Regression Results
==============================================================================
Dep. Variable:
BW
R-squared:
0.877
Model:
OLS
Adj. R-squared:
0.870
Method:
Least Squares
F-statistic:
160.8
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
1.50e-62
Time:
14:44:10
Log-Likelihood:
323.22
No. Observations:
144
AIC:
-630.4
Df Residuals:
136
BIC:
-606.7
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0031
0.002
-1.350
0.177
-0.008
0.001
Rm-Rf
0.8998
0.064
13.990
0.000
0.774
1.026
SMBP
0.1720
0.081
2.118
0.034
0.013
0.331
HML
0.0146
0.061
0.239
0.811
-0.105
0.134
RMW
-0.4105
0.090
-4.548
0.000
-0.587
-0.234
CMA
-0.0854
0.067
-1.280
0.201
-0.216
0.045
PMU
0.2094
0.064
3.254
0.001
0.083
0.335
IMTP
0.0243
0.074
0.328
0.743
-0.121
0.169
==============================================================================
Omnibus:
0.232
Durbin-Watson:
2.153
Prob(Omnibus):
0.891
Jarque-Bera (JB):
0.043
Skew:
0.013
Prob(JB):
0.979
Kurtosis:
3.080
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
---
Regression results for BN2:
OLS Regression Results
==============================================================================
Dep. Variable:
BN2
R-squared:
0.869
Model:
OLS
Adj. R-squared:
0.862
Method:
Least Squares
F-statistic:
293.1
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
9.61e-79
Time:
14:44:10
Log-Likelihood:
345.15
No. Observations:
144
AIC:
-674.3
Df Residuals:
136
BIC:
-650.6
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0046
0.002
-2.298
0.022
-0.009
-0.001
Rm-Rf
0.9569
0.043
22.255
0.000
0.873
1.041
SMBP
-0.1554
0.073
-2.137
0.033
-0.298
-0.013
HML
-0.0140
0.069
-0.204
0.838
-0.149
0.121
RMW
-0.1008
0.055
-1.830
0.067
-0.209
0.007
CMA
-0.0252
0.080
-0.315
0.753
-0.182
0.131
PMU
0.0485
0.051
0.955
0.340
-0.051
0.148
IMTP
-0.0965
0.047
-2.033
0.042
-0.190
-0.003
==============================================================================
Omnibus:
36.851
Durbin-Watson:
1.657
Prob(Omnibus):
0.000
Jarque-Bera (JB):
122.677
Skew:
-0.905
Prob(JB):
2.30e-27
Kurtosis:
7.144
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for BR:
OLS Regression Results
==============================================================================
Dep. Variable:
BR
R-squared:
0.840
Model:
OLS
Adj. R-squared:
0.831
Method:
Least Squares
F-statistic:
91.91
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
2.11e-48
Time:
14:44:10
Log-Likelihood:
359.10
No. Observations:
144
AIC:
-702.2
Df Residuals:
136
BIC:
-678.4
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0012
0.002
-0.739
0.460
-0.004
0.002
Rm-Rf
0.8462
0.044
19.256
0.000
0.760
0.932
SMBP
0.0431
0.065
0.659
0.510
-0.085
0.171
HML
-0.0705
0.040
-1.764
0.078
-0.149
0.008
RMW
0.1086
0.060
1.814
0.070
-0.009
0.226
CMA
-0.0085
0.054
-0.159
0.874
-0.113
0.096
PMU
-0.0041
0.036
-0.115
0.908
-0.074
0.066
IMTP
0.0379
0.051
0.742
0.458
-0.062
0.138
==============================================================================
Omnibus:
6.158
Durbin-Watson:
2.092
Prob(Omnibus):
0.046
Jarque-Bera (JB):
7.322
Skew:
0.272
Prob(JB):
0.0257
Kurtosis:
3.961
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for SC:
OLS Regression Results
==============================================================================
Dep. Variable:
SC
R-squared:
0.886
Model:
OLS
Adj. R-squared:
0.880
Method:
Least Squares
F-statistic:
112.1
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
2.68e-53
Time:
14:44:10
Log-Likelihood:
326.03
No. Observations:
144
AIC:
-636.1
Df Residuals:
136
BIC:
-612.3
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
0.0009
0.002
0.426
0.670
-0.003
0.005
Rm-Rf
0.8180
0.059
13.942
0.000
0.703
0.933
SMBP
0.9781
0.090
10.877
0.000
0.802
1.154
HML
0.1105
0.077
1.428
0.153
-0.041
0.262
RMW
-0.1402
0.085
-1.648
0.099
-0.307
0.027
CMA
0.5582
0.087
6.413
0.000
0.388
0.729
PMU
0.1418
0.049
2.919
0.004
0.047
0.237
IMTP
0.1276
0.051
2.499
0.012
0.028
0.228
==============================================================================
Omnibus:
6.318
Durbin-Watson:
2.050
Prob(Omnibus):
0.042
Jarque-Bera (JB):
10.442
Skew:
-0.027
Prob(JB):
0.00540
Kurtosis:
4.318
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for SN3:
OLS Regression Results
==============================================================================
Dep. Variable:
SN3
R-squared:
0.865
Model:
OLS
Adj. R-squared:
0.858
Method:
Least Squares
F-statistic:
123.8
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
8.67e-56
Time:
14:44:10
Log-Likelihood:
315.59
No. Observations:
144
AIC:
-615.2
Df Residuals:
136
BIC:
-591.4
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0007
0.002
-0.281
0.779
-0.005
0.004
Rm-Rf
0.9627
0.078
12.404
0.000
0.811
1.115
SMBP
1.0652
0.098
10.910
0.000
0.874
1.257
HML
0.0036
0.076
0.047
0.963
-0.146
0.153
RMW
-0.1770
0.088
-2.018
0.044
-0.349
-0.005
CMA
0.0591
0.104
0.571
0.568
-0.144
0.262
PMU
-0.0101
0.071
-0.143
0.886
-0.149
0.129
IMTP
-0.0851
0.056
-1.506
0.132
-0.196
0.026
==============================================================================
Omnibus:
2.825
Durbin-Watson:
2.141
Prob(Omnibus):
0.243
Jarque-Bera (JB):
2.656
Skew:
0.132
Prob(JB):
0.265
Kurtosis:
3.611
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for SA:
OLS Regression Results
==============================================================================
Dep. Variable:
SA
R-squared:
0.877
Model:
OLS
Adj. R-squared:
0.870
Method:
Least Squares
F-statistic:
208.7
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
1.79e-69
Time:
14:44:10
Log-Likelihood:
308.97
No. Observations:
144
AIC:
-601.9
Df Residuals:
136
BIC:
-578.2
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0069
0.002
-2.908
0.004
-0.012
-0.002
Rm-Rf
0.8638
0.065
13.313
0.000
0.737
0.991
SMBP
0.9302
0.097
9.586
0.000
0.740
1.120
HML
0.0547
0.066
0.824
0.410
-0.075
0.185
RMW
-0.1209
0.087
-1.388
0.165
-0.292
0.050
CMA
-0.8089
0.085
-9.571
0.000
-0.975
-0.643
PMU
0.1833
0.061
3.016
0.003
0.064
0.302
IMTP
0.0069
0.075
0.092
0.927
-0.140
0.153
==============================================================================
Omnibus:
4.245
Durbin-Watson:
2.147
Prob(Omnibus):
0.120
Jarque-Bera (JB):
4.657
Skew:
0.182
Prob(JB):
0.0974
Kurtosis:
3.803
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
---
Regression results for BC:
OLS Regression Results
==============================================================================
Dep. Variable:
BC
R-squared:
0.826
Model:
OLS
Adj. R-squared:
0.818
Method:
Least Squares
F-statistic:
73.87
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
3.17e-43
Time:
14:44:10
Log-Likelihood:
319.22
No. Observations:
144
AIC:
-622.4
Df Residuals:
136
BIC:
-598.7
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0057
0.002
-2.400
0.016
-0.010
-0.001
Rm-Rf
0.9196
0.060
15.329
0.000
0.802
1.037
SMBP
-0.1061
0.086
-1.234
0.217
-0.275
0.063
HML
-0.0756
0.071
-1.066
0.287
-0.215
0.063
RMW
-0.0837
0.073
-1.147
0.251
-0.227
0.059
CMA
0.2776
0.093
2.989
0.003
0.096
0.460
PMU
0.1247
0.059
2.128
0.033
0.010
0.240
IMTP
-0.1063
0.067
-1.585
0.113
-0.238
0.025
==============================================================================
Omnibus:
11.291
Durbin-Watson:
1.806
Prob(Omnibus):
0.004
Jarque-Bera (JB):
29.510
Skew:
0.007
Prob(JB):
3.91e-07
Kurtosis:
5.218
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for BN3:
OLS Regression Results
==============================================================================
Dep. Variable:
BN3
R-squared:
0.849
Model:
OLS
Adj. R-squared:
0.841
Method:
Least Squares
F-statistic:
153.0
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
3.00e-61
Time:
14:44:10
Log-Likelihood:
346.05
No. Observations:
144
AIC:
-676.1
Df Residuals:
136
BIC:
-652.3
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0008
0.002
-0.398
0.691
-0.004
0.003
Rm-Rf
0.9332
0.047
19.973
0.000
0.842
1.025
SMBP
0.0529
0.071
0.740
0.459
-0.087
0.193
HML
-0.0402
0.043
-0.926
0.354
-0.125
0.045
RMW
-0.0835
0.060
-1.391
0.164
-0.201
0.034
CMA
0.0096
0.050
0.192
0.848
-0.088
0.108
PMU
-0.0233
0.045
-0.515
0.607
-0.112
0.065
IMTP
0.0075
0.049
0.153
0.879
-0.089
0.104
==============================================================================
Omnibus:
19.546
Durbin-Watson:
2.213
Prob(Omnibus):
0.000
Jarque-Bera (JB):
45.824
Skew:
0.524
Prob(JB):
1.12e-10
Kurtosis:
5.557
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for BA:
OLS Regression Results
==============================================================================
Dep. Variable:
BA
R-squared:
0.864
Model:
OLS
Adj. R-squared:
0.857
Method:
Least Squares
F-statistic:
123.4
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
1.02e-55
Time:
14:44:10
Log-Likelihood:
346.08
No. Observations:
144
AIC:
-676.2
Df Residuals:
136
BIC:
-652.4
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
0.0021
0.002
1.124
0.261
-0.002
0.006
Rm-Rf
0.8738
0.054
16.111
0.000
0.768
0.980
SMBP
-0.0582
0.069
-0.839
0.401
-0.194
0.078
HML
-0.0198
0.060
-0.329
0.742
-0.138
0.098
RMW
-0.1030
0.060
-1.724
0.085
-0.220
0.014
CMA
-0.3553
0.069
-5.184
0.000
-0.490
-0.221
PMU
0.0832
0.045
1.832
0.067
-0.006
0.172
IMTP
0.0144
0.047
0.308
0.758
-0.077
0.106
==============================================================================
Omnibus:
2.739
Durbin-Watson:
1.831
Prob(Omnibus):
0.254
Jarque-Bera (JB):
2.766
Skew:
-0.034
Prob(JB):
0.251
Kurtosis:
3.676
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for SP:
OLS Regression Results
==============================================================================
Dep. Variable:
SP
R-squared:
0.941
Model:
OLS
Adj. R-squared:
0.938
Method:
Least Squares
F-statistic:
409.4
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
4.56e-88
Time:
14:44:10
Log-Likelihood:
324.59
No. Observations:
144
AIC:
-633.2
Df Residuals:
136
BIC:
-609.4
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0031
0.002
-1.371
0.170
-0.008
0.001
Rm-Rf
0.8040
0.047
17.073
0.000
0.712
0.896
SMBP
1.1296
0.093
12.113
0.000
0.947
1.312
HML
0.1748
0.069
2.519
0.012
0.039
0.311
RMW
-0.1988
0.071
-2.816
0.005
-0.337
-0.060
CMA
0.1724
0.073
2.360
0.018
0.029
0.316
PMU
0.6873
0.048
14.464
0.000
0.594
0.780
IMTP
0.0470
0.057
0.819
0.413
-0.065
0.159
==============================================================================
Omnibus:
0.799
Durbin-Watson:
2.005
Prob(Omnibus):
0.671
Jarque-Bera (JB):
0.432
Skew:
0.067
Prob(JB):
0.806
Kurtosis:
3.232
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for SN4:
OLS Regression Results
==============================================================================
Dep. Variable:
SN4
R-squared:
0.867
Model:
OLS
Adj. R-squared:
0.860
Method:
Least Squares
F-statistic:
138.3
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
1.29e-58
Time:
14:44:10
Log-Likelihood:
311.06
No. Observations:
144
AIC:
-606.1
Df Residuals:
136
BIC:
-582.4
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
0.0008
0.002
0.317
0.751
-0.004
0.005
Rm-Rf
1.0745
0.064
16.730
0.000
0.949
1.200
SMBP
1.0153
0.080
12.670
0.000
0.858
1.172
HML
-0.0641
0.062
-1.028
0.304
-0.186
0.058
RMW
-0.0198
0.088
-0.226
0.821
-0.191
0.152
CMA
-0.1252
0.067
-1.882
0.060
-0.256
0.005
PMU
-0.0078
0.060
-0.129
0.897
-0.126
0.110
IMTP
-0.0328
0.068
-0.483
0.629
-0.166
0.100
==============================================================================
Omnibus:
1.032
Durbin-Watson:
2.220
Prob(Omnibus):
0.597
Jarque-Bera (JB):
0.811
Skew:
0.182
Prob(JB):
0.667
Kurtosis:
3.057
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
---
Regression results for SU:
OLS Regression Results
==============================================================================
Dep. Variable:
SU
R-squared:
0.778
Model:
OLS
Adj. R-squared:
0.767
Method:
Least Squares
F-statistic:
42.36
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
3.30e-31
Time:
14:44:10
Log-Likelihood:
346.86
No. Observations:
144
AIC:
-677.7
Df Residuals:
136
BIC:
-654.0
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0040
0.002
-1.835
0.067
-0.008
0.000
Rm-Rf
0.7921
0.065
12.117
0.000
0.664
0.920
SMBP
0.8246
0.090
9.123
0.000
0.647
1.002
HML
0.1397
0.050
2.800
0.005
0.042
0.238
RMW
-0.2503
0.062
-4.057
0.000
-0.371
-0.129
CMA
0.0168
0.081
0.206
0.836
-0.143
0.176
PMU
-0.5088
0.061
-8.277
0.000
-0.629
-0.388
IMTP
-0.0172
0.060
-0.288
0.774
-0.134
0.100
==============================================================================
Omnibus:
9.206
Durbin-Watson:
1.846
Prob(Omnibus):
0.010
Jarque-Bera (JB):
10.584
Skew:
0.443
Prob(JB):
0.00503
Kurtosis:
3.989
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for BP:
OLS Regression Results
==============================================================================
Dep. Variable:
BP
R-squared:
0.909
Model:
OLS
Adj. R-squared:
0.905
Method:
Least Squares
F-statistic:
193.6
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
1.85e-67
Time:
14:44:10
Log-Likelihood:
325.19
No. Observations:
144
AIC:
-634.4
Df Residuals:
136
BIC:
-610.6
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
0.0002
0.002
0.093
0.926
-0.004
0.005
Rm-Rf
0.8715
0.070
12.433
0.000
0.734
1.009
SMBP
-0.1730
0.091
-1.900
0.057
-0.351
0.005
HML
-0.0003
0.051
-0.006
0.995
-0.100
0.100
RMW
-0.0834
0.067
-1.240
0.215
-0.215
0.048
CMA
-0.0712
0.084
-0.844
0.399
-0.237
0.094
PMU
0.5924
0.064
9.266
0.000
0.467
0.718
IMTP
0.0009
0.066
0.014
0.989
-0.128
0.130
==============================================================================
Omnibus:
2.619
Durbin-Watson:
1.837
Prob(Omnibus):
0.270
Jarque-Bera (JB):
2.260
Skew:
0.301
Prob(JB):
0.323
Kurtosis:
3.118
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for BN4:
OLS Regression Results
==============================================================================
Dep. Variable:
BN4
R-squared:
0.869
Model:
OLS
Adj. R-squared:
0.862
Method:
Least Squares
F-statistic:
288.7
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
2.52e-78
Time:
14:44:10
Log-Likelihood:
345.26
No. Observations:
144
AIC:
-674.5
Df Residuals:
136
BIC:
-650.8
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0047
0.002
-2.336
0.020
-0.009
-0.001
Rm-Rf
0.9576
0.043
22.335
0.000
0.874
1.042
SMBP
-0.1477
0.073
-2.031
0.042
-0.290
-0.005
HML
-0.0108
0.069
-0.157
0.875
-0.146
0.124
RMW
-0.1021
0.055
-1.856
0.063
-0.210
0.006
CMA
-0.0232
0.079
-0.292
0.770
-0.179
0.133
PMU
0.0453
0.051
0.892
0.372
-0.054
0.145
IMTP
-0.1040
0.047
-2.203
0.028
-0.197
-0.011
==============================================================================
Omnibus:
36.824
Durbin-Watson:
1.674
Prob(Omnibus):
0.000
Jarque-Bera (JB):
124.860
Skew:
-0.897
Prob(JB):
7.71e-28
Kurtosis:
7.194
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for BU:
OLS Regression Results
==============================================================================
Dep. Variable:
BU
R-squared:
0.782
Model:
OLS
Adj. R-squared:
0.771
Method:
Least Squares
F-statistic:
87.25
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
3.77e-47
Time:
14:44:10
Log-Likelihood:
344.69
No. Observations:
144
AIC:
-673.4
Df Residuals:
136
BIC:
-649.6
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
0.0011
0.002
0.620
0.535
-0.002
0.005
Rm-Rf
0.8834
0.045
19.851
0.000
0.796
0.971
SMBP
0.1321
0.067
1.958
0.050
-0.000
0.264
HML
0.0347
0.049
0.706
0.480
-0.062
0.131
RMW
-0.0319
0.057
-0.557
0.577
-0.144
0.080
CMA
0.0843
0.053
1.596
0.111
-0.019
0.188
PMU
-0.2115
0.040
-5.295
0.000
-0.290
-0.133
IMTP
0.0651
0.049
1.338
0.181
-0.030
0.160
==============================================================================
Omnibus:
6.261
Durbin-Watson:
2.114
Prob(Omnibus):
0.044
Jarque-Bera (JB):
10.248
Skew:
0.039
Prob(JB):
0.00595
Kurtosis:
4.305
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for PI:
OLS Regression Results
==============================================================================
Dep. Variable:
PI
R-squared:
0.956
Model:
OLS
Adj. R-squared:
0.954
Method:
Least Squares
F-statistic:
495.0
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
1.95e-93
Time:
14:44:10
Log-Likelihood:
359.59
No. Observations:
144
AIC:
-703.2
Df Residuals:
136
BIC:
-679.4
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0013
0.002
-0.670
0.503
-0.005
0.002
Rm-Rf
0.8662
0.050
17.465
0.000
0.769
0.963
SMBP
0.6775
0.073
9.343
0.000
0.535
0.820
HML
0.1122
0.046
2.423
0.015
0.021
0.203
RMW
-0.1442
0.055
-2.614
0.009
-0.252
-0.036
CMA
-0.0060
0.061
-0.098
0.922
-0.126
0.114
PMU
0.6307
0.048
13.138
0.000
0.537
0.725
IMTP
0.2985
0.043
6.915
0.000
0.214
0.383
==============================================================================
Omnibus:
1.608
Durbin-Watson:
1.839
Prob(Omnibus):
0.448
Jarque-Bera (JB):
1.234
Skew:
0.038
Prob(JB):
0.540
Kurtosis:
3.447
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
---
Regression results for UI:
OLS Regression Results
==============================================================================
Dep. Variable:
UI
R-squared:
0.759
Model:
OLS
Adj. R-squared:
0.747
Method:
Least Squares
F-statistic:
60.45
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
1.10e-38
Time:
14:44:10
Log-Likelihood:
348.59
No. Observations:
144
AIC:
-681.2
Df Residuals:
136
BIC:
-657.4
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0006
0.002
-0.336
0.737
-0.004
0.003
Rm-Rf
0.7857
0.052
15.117
0.000
0.684
0.888
SMBP
0.4168
0.081
5.162
0.000
0.259
0.575
HML
0.0593
0.051
1.163
0.245
-0.041
0.159
RMW
-0.1112
0.055
-2.006
0.045
-0.220
-0.003
CMA
0.0960
0.066
1.463
0.143
-0.033
0.225
PMU
-0.3009
0.047
-6.370
0.000
-0.393
-0.208
IMTP
0.2587
0.059
4.407
0.000
0.144
0.374
==============================================================================
Omnibus:
16.260
Durbin-Watson:
2.347
Prob(Omnibus):
0.000
Jarque-Bera (JB):
26.940
Skew:
0.555
Prob(JB):
1.41e-06
Kurtosis:
4.804
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for PT:
OLS Regression Results
==============================================================================
Dep. Variable:
PT
R-squared:
0.890
Model:
OLS
Adj. R-squared:
0.885
Method:
Least Squares
F-statistic:
199.4
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
2.95e-68
Time:
14:44:10
Log-Likelihood:
286.69
No. Observations:
144
AIC:
-557.4
Df Residuals:
136
BIC:
-533.6
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
0.0008
0.003
0.303
0.762
-0.004
0.006
Rm-Rf
0.7301
0.082
8.905
0.000
0.569
0.891
SMBP
0.6820
0.129
5.281
0.000
0.429
0.935
HML
0.0663
0.072
0.923
0.356
-0.074
0.207
RMW
-0.0991
0.084
-1.186
0.236
-0.263
0.065
CMA
0.1140
0.105
1.084
0.278
-0.092
0.320
PMU
0.6960
0.076
9.174
0.000
0.547
0.845
IMTP
-1.0895
0.113
-9.679
0.000
-1.310
-0.869
==============================================================================
Omnibus:
5.299
Durbin-Watson:
2.434
Prob(Omnibus):
0.071
Jarque-Bera (JB):
5.984
Skew:
0.245
Prob(JB):
0.0502
Kurtosis:
3.870
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
--Regression results for UT:
OLS Regression Results
==============================================================================
Dep. Variable:
UT
R-squared:
0.738
Model:
OLS
Adj. R-squared:
0.725
Method:
Least Squares
F-statistic:
63.77
Date:
Sat, 30 Dec 2023
Prob (F-statistic):
7.10e-40
Time:
14:44:10
Log-Likelihood:
317.76
No. Observations:
144
AIC:
-619.5
Df Residuals:
136
BIC:
-595.8
Df Model:
7
Covariance Type:
HAC
==============================================================================
coef
std err
z
P>|z|
[0.025
0.975]
-----------------------------------------------------------------------------const
-0.0027
0.003
-1.016
0.309
-0.008
0.002
Rm-Rf
0.9218
0.061
14.999
0.000
0.801
1.042
SMBP
0.4123
0.099
4.166
0.000
0.218
0.606
HML
0.1052
0.055
1.903
0.057
-0.003
0.213
RMW
-0.1563
0.068
-2.291
0.022
-0.290
-0.023
CMA
-0.0240
0.072
-0.332
0.740
-0.166
0.118
PMU
-0.3661
0.067
-5.493
0.000
-0.497
-0.235
IMTP
-0.3532
0.076
-4.666
0.000
-0.502
-0.205
==============================================================================
Omnibus:
1.192
Durbin-Watson:
1.692
Prob(Omnibus):
0.551
Jarque-Bera (JB):
1.180
Skew:
0.215
Prob(JB):
0.554
Kurtosis:
2.892
Cond. No.
38.1
==============================================================================
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 l
ags and without small sample correction
---