INF-Cointegration Series
July 16, 2021
Copyright By PowCoder代写 加微信 powcoder
1 Importing packages
[1]: #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
2 Reading Excel file saved in hard drive
[2]: #reading the file
df = pd.read_excel(“C:\\Users\\rluck\\OneDrive\\fisher_update.xlsx”)
[2]: DATE P R
0 1969-12-01 17.1 5.65
1 1970-03-01 17.3 7.15
2 1970-06-01 17.5 8.70
3 1970-09-01 17.6 6.35
4 1970-12-01 17.9 6.50
166 2011-06-01 178.3 4.99
167 2011-09-01 179.4 4.81
168 2011-12-01 179.4 4.51
169 2012-03-01 179.5 4.44
170 2012-06-01 180.4 3.49
[171 rows x 3 columns]
3 Calculating annual inflation from quarterly CPI
Quarterly CPI:
INFqtr = 100 ∗ ln(Pt/Pt−1)
Annual CPI
INFqtr = 400 ∗ ln(Pt/Pt−1)
[3]: #computing the inflation rate
df[‘INF’] = 400*np.log(df[‘P’]/df[‘P’].shift(1))
[3]: DATE P R INF
0 1969-12-01 17.1 5.65 NaN
1 1970-03-01 17.3 7.15 4.651215
2 1970-06-01 17.5 8.70 4.597752
3 1970-09-01 17.6 6.35 2.279208
4 1970-12-01 17.9 6.50 6.760724
.. … … … …
166 2011-06-01 178.3 4.99 3.605658
167 2011-09-01 179.4 4.81 2.460170
168 2011-12-01 179.4 4.51 0.000000
169 2012-03-01 179.5 4.44 0.222903
170 2012-06-01 180.4 3.49 2.000560
[171 rows x 4 columns]
[4]: # Generating integrating differences series
df[‘DINF’] = df[‘INF’].diff(1).dropna()
df[‘DINF1’] = df[‘DINF’].shift(1).dropna()
df[‘DINF2’] = df[‘DINF’].shift(2).dropna()
df[‘DINF3’] = df[‘DINF’].shift(3).dropna()
df[‘DINF4’] = df[‘DINF’].shift(4).dropna()
df[‘DR’] = df[‘R’].diff(1).dropna()
df[‘DR1’] = df[‘DR’].shift(1).dropna()
df[‘DR2’] = df[‘DR’].shift(2).dropna()
df[‘DR3’] = df[‘DR’].shift(3).dropna()
df[‘DR4’] = df[‘DR’].shift(4).dropna()
df.head(60)
[4]: DATE P R INF DINF DINF1 DINF2 \
0 1969-12-01 17.1 5.65 NaN NaN NaN NaN
1 1970-03-01 17.3 7.15 4.651215 NaN NaN NaN
2 1970-06-01 17.5 8.70 4.597752 -0.053463 NaN NaN
3 1970-09-01 17.6 6.35 2.279208 -2.318543 -0.053463 NaN
4 1970-12-01 17.9 6.50 6.760724 4.481516 -2.318543 -0.053463
5 1971-03-01 18.1 8.00 4.444490 -2.316234 4.481516 -2.318543
6 1971-06-01 18.4 8.15 6.575491 2.131000 -2.316234 4.481516
7 1971-09-01 18.8 6.45 8.602482 2.026992 2.131000 -2.316234
8 1971-12-01 19.2 5.90 8.421364 -0.181118 2.026992 2.131000
9 1972-03-01 19.4 5.50 4.145115 -4.276249 -0.181118 2.026992
10 1972-06-01 19.6 5.75 4.102600 -0.042515 -4.276249 -0.181118
11 1972-09-01 19.9 4.50 6.076066 1.973466 -0.042515 -4.276249
12 1972-12-01 20.1 4.45 4.000033 -2.076033 1.973466 -0.042515
13 1973-03-01 20.5 5.45 7.882028 3.881995 -2.076033 1.973466
14 1973-06-01 21.2 6.40 13.430518 5.548490 3.881995 -2.076033
15 1973-09-01 21.9 9.25 12.994182 -0.436336 5.548490 3.881995
16 1973-12-01 22.7 9.25 14.351315 1.357133 -0.436336 5.548490
17 1974-03-01 23.3 10.10 10.435374 -3.915941 1.357133 -0.436336
18 1974-06-01 24.3 18.80 16.809196 6.373821 -3.915941 1.357133
19 1974-09-01 25.5 12.60 19.280841 2.471645 6.373821 -3.915941
20 1974-12-01 26.4 9.75 13.874223 -5.406618 2.471645 6.373821
21 1975-03-01 27.4 8.75 14.871601 0.997378 -5.406618 2.471645
22 1975-06-01 28.4 8.80 14.338453 -0.533149 0.997378 -5.406618
23 1975-09-01 28.6 8.10 2.807029 -11.531424 -0.533149 0.997378
24 1975-12-01 30.2 7.70 21.774083 18.967054 -11.531424 -0.533149
25 1976-03-01 31.0 8.40 10.458112 -11.315971 18.967054 -11.531424
26 1976-06-01 31.8 10.27 10.191634 -0.266478 -11.315971 18.967054
27 1976-09-01 32.6 9.31 9.938399 -0.253235 -0.266478 -11.315971
28 1976-12-01 34.5 9.44 22.658814 12.720415 -0.253235 -0.266478
29 1977-03-01 35.3 9.73 9.169456 -13.489358 12.720415 -0.253235
30 1977-06-01 36.1 10.95 8.963961 -0.205495 -13.489358 12.720415
31 1977-09-01 36.8 10.43 7.681992 -1.281969 -0.205495 -13.489358
32 1977-12-01 37.7 9.75 9.664900 1.982908 -1.281969 -0.205495
33 1978-03-01 38.2 10.04 5.270168 -4.394731 1.982908 -1.281969
34 1978-06-01 39.0 10.63 8.290452 3.020284 -4.394731 1.982908
35 1978-09-01 39.7 9.72 7.115817 -1.174636 3.020284 -4.394731
36 1978-12-01 40.6 8.76 8.966752 1.850935 -1.174636 3.020284
37 1979-03-01 41.3 9.16 6.837773 -2.128978 1.850935 -1.174636
38 1979-06-01 42.4 10.26 10.514345 3.676572 -2.128978 1.850935
39 1979-09-01 43.4 9.87 9.324432 -1.189913 3.676572 -2.128978
40 1979-12-01 44.7 10.12 11.805624 2.481193 -1.189913 3.676572
41 1980-03-01 45.7 11.47 8.849919 -2.955706 2.481193 -1.189913
42 1980-06-01 47.0 13.83 11.219722 2.369803 -2.955706 2.481193
43 1980-09-01 47.8 11.69 6.751215 -4.468506 2.369803 -2.955706
44 1980-12-01 48.8 12.45 8.281869 1.530654 -4.468506 2.369803
45 1981-03-01 50.0 14.63 9.717077 1.435208 1.530654 -4.468506
46 1981-06-01 51.1 15.58 8.704597 -1.012480 1.435208 1.530654
47 1981-09-01 52.1 15.35 7.752181 -0.952416 -1.012480 1.435208
48 1981-12-01 54.3 15.54 16.543711 8.791531 -0.952416 -1.012480
49 1982-03-01 55.3 18.89 7.299473 -9.244239 8.791531 -0.952416
50 1982-06-01 56.6 18.57 9.294431 1.994958 -9.244239 8.791531
51 1982-09-01 58.6 15.46 13.890285 4.595854 1.994958 -9.244239
52 1982-12-01 60.3 12.13 11.438963 -2.451322 4.595854 1.994958
53 1983-03-01 61.6 15.26 8.531907 -2.907056 -2.451322 4.595854
54 1983-06-01 62.9 14.24 8.353717 -0.178189 -2.907056 -2.451322
55 1983-09-01 64.0 11.06 6.934768 -1.418949 -0.178189 -2.907056
56 1983-12-01 65.5 8.89 9.266824 2.332056 -1.418949 -0.178189
57 1984-03-01 65.2 13.77 -1.836269 -11.103093 2.332056 -1.418949
58 1984-06-01 65.4 12.81 1.225116 3.061385 -11.103093 2.332056
59 1984-09-01 66.2 10.53 4.863282 3.638166 3.061385 -11.103093
DINF3 DINF4 DR DR1 DR2 DR3 DR4
0 NaN NaN NaN NaN NaN NaN NaN
1 NaN NaN 1.50 NaN NaN NaN NaN
2 NaN NaN 1.55 1.50 NaN NaN NaN
3 NaN NaN -2.35 1.55 1.50 NaN NaN
4 NaN NaN 0.15 -2.35 1.55 1.50 NaN
5 -0.053463 NaN 1.50 0.15 -2.35 1.55 1.50
6 -2.318543 -0.053463 0.15 1.50 0.15 -2.35 1.55
7 4.481516 -2.318543 -1.70 0.15 1.50 0.15 -2.35
8 -2.316234 4.481516 -0.55 -1.70 0.15 1.50 0.15
9 2.131000 -2.316234 -0.40 -0.55 -1.70 0.15 1.50
10 2.026992 2.131000 0.25 -0.40 -0.55 -1.70 0.15
11 -0.181118 2.026992 -1.25 0.25 -0.40 -0.55 -1.70
12 -4.276249 -0.181118 -0.05 -1.25 0.25 -0.40 -0.55
13 -0.042515 -4.276249 1.00 -0.05 -1.25 0.25 -0.40
14 1.973466 -0.042515 0.95 1.00 -0.05 -1.25 0.25
15 -2.076033 1.973466 2.85 0.95 1.00 -0.05 -1.25
16 3.881995 -2.076033 0.00 2.85 0.95 1.00 -0.05
17 5.548490 3.881995 0.85 0.00 2.85 0.95 1.00
18 -0.436336 5.548490 8.70 0.85 0.00 2.85 0.95
19 1.357133 -0.436336 -6.20 8.70 0.85 0.00 2.85
20 -3.915941 1.357133 -2.85 -6.20 8.70 0.85 0.00
21 6.373821 -3.915941 -1.00 -2.85 -6.20 8.70 0.85
22 2.471645 6.373821 0.05 -1.00 -2.85 -6.20 8.70
23 -5.406618 2.471645 -0.70 0.05 -1.00 -2.85 -6.20
24 0.997378 -5.406618 -0.40 -0.70 0.05 -1.00 -2.85
25 -0.533149 0.997378 0.70 -0.40 -0.70 0.05 -1.00
26 -11.531424 -0.533149 1.87 0.70 -0.40 -0.70 0.05
27 18.967054 -11.531424 -0.96 1.87 0.70 -0.40 -0.70
28 -11.315971 18.967054 0.13 -0.96 1.87 0.70 -0.40
29 -0.266478 -11.315971 0.29 0.13 -0.96 1.87 0.70
30 -0.253235 -0.266478 1.22 0.29 0.13 -0.96 1.87
31 12.720415 -0.253235 -0.52 1.22 0.29 0.13 -0.96
32 -13.489358 12.720415 -0.68 -0.52 1.22 0.29 0.13
33 -0.205495 -13.489358 0.29 -0.68 -0.52 1.22 0.29
34 -1.281969 -0.205495 0.59 0.29 -0.68 -0.52 1.22
35 1.982908 -1.281969 -0.91 0.59 0.29 -0.68 -0.52
36 -4.394731 1.982908 -0.96 -0.91 0.59 0.29 -0.68
37 3.020284 -4.394731 0.40 -0.96 -0.91 0.59 0.29
38 -1.174636 3.020284 1.10 0.40 -0.96 -0.91 0.59
39 1.850935 -1.174636 -0.39 1.10 0.40 -0.96 -0.91
40 -2.128978 1.850935 0.25 -0.39 1.10 0.40 -0.96
41 3.676572 -2.128978 1.35 0.25 -0.39 1.10 0.40
42 -1.189913 3.676572 2.36 1.35 0.25 -0.39 1.10
43 2.481193 -1.189913 -2.14 2.36 1.35 0.25 -0.39
44 -2.955706 2.481193 0.76 -2.14 2.36 1.35 0.25
45 2.369803 -2.955706 2.18 0.76 -2.14 2.36 1.35
46 -4.468506 2.369803 0.95 2.18 0.76 -2.14 2.36
47 1.530654 -4.468506 -0.23 0.95 2.18 0.76 -2.14
48 1.435208 1.530654 0.19 -0.23 0.95 2.18 0.76
49 -1.012480 1.435208 3.35 0.19 -0.23 0.95 2.18
50 -0.952416 -1.012480 -0.32 3.35 0.19 -0.23 0.95
51 8.791531 -0.952416 -3.11 -0.32 3.35 0.19 -0.23
52 -9.244239 8.791531 -3.33 -3.11 -0.32 3.35 0.19
53 1.994958 -9.244239 3.13 -3.33 -3.11 -0.32 3.35
54 4.595854 1.994958 -1.02 3.13 -3.33 -3.11 -0.32
55 -2.451322 4.595854 -3.18 -1.02 3.13 -3.33 -3.11
56 -2.907056 -2.451322 -2.17 -3.18 -1.02 3.13 -3.33
57 -0.178189 -2.907056 4.88 -2.17 -3.18 -1.02 3.13
58 -1.418949 -0.178189 -0.96 4.88 -2.17 -3.18 -1.02
59 2.332056 -1.418949 -2.28 -0.96 4.88 -2.17 -3.18
4 Selecting sample data from row 57:Qtr 1 1984 to row 170: Qtr
[5]: #Selecting the sample from
dta =df.iloc[57:170].dropna()
[5]: DATE P R INF DINF DINF1 DINF2 \
57 1984-03-01 65.2 13.77 -1.836269 -11.103093 2.332056 -1.418949
58 1984-06-01 65.4 12.81 1.225116 3.061385 -11.103093 2.332056
59 1984-09-01 66.2 10.53 4.863282 3.638166 3.061385 -11.103093
60 1984-12-01 67.2 12.34 5.997114 1.133832 3.638166 3.061385
61 1985-03-01 68.1 15.29 5.321586 -0.675528 1.133832 3.638166
.. … … … … … … …
165 2011-03-01 176.7 4.92 6.159232 4.546791 -1.166956 0.214539
166 2011-06-01 178.3 4.99 3.605658 -2.553574 4.546791 -1.166956
167 2011-09-01 179.4 4.81 2.460170 -1.145488 -2.553574 4.546791
168 2011-12-01 179.4 4.51 0.000000 -2.460170 -1.145488 -2.553574
169 2012-03-01 179.5 4.44 0.222903 0.222903 -2.460170 -1.145488
DINF3 DINF4 DR DR1 DR2 DR3 DR4
57 -0.178189 -2.907056 4.88 -2.17 -3.18 -1.02 3.13
58 -1.418949 -0.178189 -0.96 4.88 -2.17 -3.18 -1.02
59 2.332056 -1.418949 -2.28 -0.96 4.88 -2.17 -3.18
60 -11.103093 2.332056 1.81 -2.28 -0.96 4.88 -2.17
61 3.061385 -11.103093 2.95 1.81 -2.28 -0.96 4.88
.. … … … … … … …
165 -0.959393 1.394699 -0.11 0.21 -0.07 0.56 0.20
166 0.214539 -0.959393 0.07 -0.11 0.21 -0.07 0.56
167 -1.166956 0.214539 -0.18 0.07 -0.11 0.21 -0.07
168 4.546791 -1.166956 -0.30 -0.18 0.07 -0.11 0.21
169 -2.553574 4.546791 -0.07 -0.30 -0.18 0.07 -0.11
[113 rows x 14 columns]
5 Plotting the time series: Inflation
[6]: #plotting the series
plt.plot(dta[‘INF’],label=’INF’)
plt.plot(dta[‘R’],label=’R’)
plt.legend(loc=’best’, fontsize=’large’)
plt.show()
[7]: #Regressing Interest Rate (Y=R) against the Inflation rate (X= INF)
reg = linear_model.LinearRegression()
X =dta[[‘INF’]].dropna()
y =dta[‘R’].dropna()
reg.fit(X,y)
predictions =reg.predict(X)
[8]: plt.xlabel(‘INF’)
plt.ylabel(‘R’)
plt.scatter(dta.INF,dta.R,color=’red’,marker=’+’)
plt.plot(dta.INF,reg.predict(dta[[‘INF’]]), color=’orange’)
[8]: [
[9]: #model with intercept
X = dta.INF
X= sm.add_constant(X)
model= sm.OLS(y,X).fit()
predictions = model.predict(X)
G= (model.summary())
OLS Regression Results
==============================================================================
Dep. Variable: R R-squared: 0.412
Model: OLS Adj. R-squared: 0.407
Method: Least Squares F-statistic: 77.80
Date: Fri, 16 Jul 2021 Prob (F-statistic): 1.83e-14
Time: 21:22:16 Log-Likelihood: -294.55
No. Observations: 113 AIC: 593.1
Df Residuals: 111 BIC: 598.5
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
——————————————————————————
const 4.8120 0.480 10.020 0.000 3.860 5.764
INF 0.9039 0.102 8.821 0.000 0.701 1.107
==============================================================================
Omnibus: 11.514 Durbin-Watson: 0.699
Prob(Omnibus): 0.003 Jarque-Bera (JB): 14.994
Skew: 0.546 Prob(JB): 0.000555
Kurtosis: 4.411 Cond. No. 7.42
==============================================================================
[1] Standard Errors assume that the covariance matrix of the errors is correctly
specified.
6 Correlogram of Residuals: ACF and PACF
ϵt = yt − (β ∗Xt + α)
[10]: dtr = model.resid
[10]: 57 10.617794
58 6.890682
59 1.322232
60 2.107389
61 5.667982
165 -5.459146
166 -3.081032
167 -2.225653
168 -0.301965
169 -0.573442
Length: 113, dtype: float64
[11]: #running ACF and PACF
sm.graphics.tsa.plot_acf(dtr.values.squeeze(),lags=16)
sm.graphics.tsa.plot_pacf(dtr.values.squeeze(),lags=16)
plt.show()
[12]: # Generating the Q tables
import numpy as np
r,q,p = sm.tsa.acf(dtr.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)
1.0 0.604164 42.351394 7.626197e-11
2.0 0.561012 79.197947 6.344308e-18
3.0 0.574160 118.142798 1.938169e-25
4.0 0.558060 155.271704 1.509379e-32
5.0 0.498832 185.212371 4.120822e-38
6.0 0.477251 212.874547 3.437139e-43
7.0 0.444019 237.044412 1.579656e-47
8.0 0.404992 257.343619 4.775363e-51
9.0 0.370545 274.499942 6.605085e-54
10.0 0.337784 288.895138 3.451093e-56
11.0 0.275816 298.587198 1.738371e-57
12.0 0.286480 309.146676 5.627670e-59
13.0 0.296186 320.546711 1.193303e-60
14.0 0.259174 329.363744 8.672219e-62
15.0 0.223192 335.969290 1.796166e-62
16.0 0.226696 342.854116 3.193704e-63
17.0 0.255196 351.669754 2.217145e-64
18.0 0.223284 358.489525 3.951410e-65
19.0 0.298762 370.829082 4.992993e-67
20.0 0.321913 385.309124 2.265168e-69
21.0 0.282732 396.600261 4.685822e-71
22.0 0.298276 409.305178 4.926778e-73
23.0 0.234833 417.267758 4.917945e-74
24.0 0.236777 425.453665 4.382705e-75
25.0 0.229401 433.224808 4.722116e-76
26.0 0.174816 437.789603 2.301703e-76
27.0 0.162803 441.794612 1.445240e-76
28.0 0.223076 449.402502 1.643747e-77
29.0 0.149866 452.877109 1.299917e-77
30.0 0.154104 456.595241 9.069163e-78
31.0 0.098993 458.148250 1.727635e-77
32.0 0.100837 459.779524 3.130430e-77
33.0 0.027877 459.905761 1.130134e-76
34.0 0.021439 459.981366 4.113627e-76
35.0 0.014447 460.016136 1.503308e-75
36.0 -0.023361 460.108237 5.272135e-75
37.0 -0.053373 460.595316 1.518910e-74
38.0 -0.062695 461.276367 3.950474e-74
39.0 -0.003679 461.278743 1.387193e-73
40.0 -0.076177 462.311755 2.995337e-73
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(
7 ADF test of stationarity and unit root
[13]: residuals = model.resid
[13]: 57 10.617794
58 6.890682
59 1.322232
60 2.107389
61 5.667982
165 -5.459146
166 -3.081032
167 -2.225653
168 -0.301965
169 -0.573442
Length: 113, dtype: float64
[14]: 57 10.617794
58 6.890682
59 1.322232
60 2.107389
61 5.667982
165 -5.459146
166 -3.081032
167 -2.225653
168 -0.301965
169 -0.573442
Length: 113, dtype: float64
[15]: #ADF Tests
from arch.unitroot import ADF
ADF(residuals,trend=”n”,lags=1, max_lags=12, method=’BIC’)
[15]:
Augmented Dickey-
=====================================
Test Statistic -3.854
P-value 0.000
————————————-
Trend: No Trend
Critical Values: -2.59 (1%), -1.94 (5%), -1.61 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.
8 Cointegration Test
[16]: from arch.unitroot import engle_granger
engle_test = engle_granger(y,X, trend =”n”,lags=1)
engle_test
[16]: Engle- Test
Statistic: -3.8538026300067636
P-value: 0.010421142946669465
Null: No Cointegration, Alternative: Cointegration
ADF Lag length: 1
Estimated Root � (�+1): 0.7108844276270996
Distribution Order: 2
ID: 0x2850f984a90
9 DR Regressed against DR & DINF with lags up to 4
ϵt = yt − (βxt + α)
[17]: dta[‘resid’] = y -model.predict(X)
#Residual series by lag 1
dta[‘resid_1’]= dta[‘resid’].shift(1)
dta = dta.dropna(subset=[‘resid_1’])
[17]: DATE P R INF DINF DINF1 DINF2 \
58 1984-06-01 65.4 12.81 1.225116 3.061385 -11.103093 2.332056
59 1984-09-01 66.2 10.53 4.863282 3.638166 3.061385 -11.103093
60 1984-12-01 67.2 12.34 5.997114 1.133832 3.638166 3.061385
61 1985-03-01 68.1 15.29 5.321586 -0.675528 1.133832 3.638166
62 1985-06-01 69.7 15.75 9.289242 3.967656 -0.675528 1.133832
.. … … … … … … …
165 2011-03-01 176.7 4.92 6.159232 4.546791 -1.166956 0.214539
166 2011-06-01 178.3 4.99 3.605658 -2.553574 4.546791 -1.166956
167 2011-09-01 179.4 4.81 2.460170 -1.145488 -2.553574 4.546791
168 2011-12-01 179.4 4.51 0.000000 -2.460170 -1.145488 -2.553574
169 2012-03-01 179.5 4.44 0.222903 0.222903 -2.460170 -1.145488
DINF3 DINF4 DR DR1 DR2 DR3 DR4 resid resid_1
58 -1.418949 -0.178189 -0.96 4.88 -2.17 -3.18 -1.02 6.890682 10.617794
59 2.332056 -1.418949 -2.28 -0.96 4.88 -2.17 -3.18 1.322232 6.890682
60 -11.103093 2.332056 1.81 -2.28 -0.96 4.88 -2.17 2.107389 1.322232
61 3.061385 -11.103093 2.95 1.81 -2.28 -0.96 4.88 5.667982 2.107389
62 3.638166 3.061385 0.46 2.95 1.81 -2.28 -0.96 2.541714 5.667982
.. … … … … … … … … …
165 -0.959393 1.394699 -0.11 0.21 -0.07 0.56 0.20 -5.459146 -1.239412
166 0.214539 -0.959393 0.07 -0.11 0.21 -0.07 0.56 -3.081032 -5.459146
167 -1.166956 0.214539 -0.18 0.07 -0.11 0.21 -0.07 -2.225653 -3.081032
168 4.546791 -1.166956 -0.30 -0.18 0.07 -0.11 0.21 -0.301965 -2.225653
169 -2.553574 4.546791 -0.07 -0.30 -0.18 0.07 -0.11 -0.573442 -0.301965
[112 rows x 16 columns]
Multiple Regression
[18]: #model with intercept
x_1 = dta[[‘resid_1′,’DR1′,’DR2′,’DR3′,’DR4′,’DINF1′,’DINF2′,’DINF3′,’DINF4’]]
y_1 = dta[‘DR’]
x_1= sm.add_constant(x_1)
model_1 = sm.OLS(y_1,x_1).fit()
predictions = model_1.predict(x_1)
h= (model_1.summary())
OLS Regression Results
==============================================================================
Dep. Variable: DR R-squared: 0.189
Model: OLS Adj. R-squared: 0.117
Method: Least Squares F-statistic: 2.633
Date: Fri, 16 Jul 2021 Prob (F-statistic): 0.00881
Time: 21:22:17 Log-Likelihood: -151.97
No. Observations: 112 AIC: 323.9
Df Residuals: 102 BIC: 351.1
Df Model: 9
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
——————————————————————————
const -0.0631 0.094 -0.674 0.502 -0.249 0.123
resid_1 -0.0579 0.035 -1.631 0.106 -0.128 0.012
DR1 0.1464 0.091 1.613 0.110 -0.034 0.327
DR2 0.0222 0.091 0.243 0.808 -0.159 0.203
DR3 0.2249 0.085 2.653 0.009 0.057 0.393
DR4 -0.0686 0.082 -0.833 0.407 -0.232 0.095
DINF1 0.0264 0.047 0.558 0.578 -0.067 0.120
DINF2 0.0365 0.051 0.717 0.475 -0.064 0.137
DINF3 -0.0415 0.049 -0.843 0.401 -0.139 0.056
DINF4 -0.0570 0.040 -1.425 0.157 -0.136 0.022
==============================================================================
Omnibus: 15.294 Durbin-Watson: 2.004
Prob(Omnibus): 0.000 Jarque-Bera (JB): 59.082
Skew: 0.087 Prob(JB): 1.48e-13
Kurtosis: 6.554 Cond. No. 5.07
==============================================================================
[1] Standard Errors assume that the covariance matrix of the errors is correctly
specified.
10 DINF Regressed against DR & DINF with lags up to 4
[19]: #model with intercept
x_1 = dta[[‘resid_1′,’DR1′,’DR2′,’DR3′,’DR4′,’DINF1′,’DINF2′,’DINF3′,’DINF4’]]
y_2 = dta[‘DINF’]
x_1= sm.add_constant(x_1)
model_2 = sm.OLS(y_2,x_1).fit()
predictions = model_2.predict(x_1)
I= (model_2.summary())
OLS Regression Results
==============================================================================
Dep. Variable: DINF R-squared: 0.367
Model: OLS Adj. R-squared: 0.311
Method: Least Squares F-statistic: 6.574
Date: Fri, 16 Jul 2021 Prob (F-statistic): 2.36e-07
Time: 21:22:17 Log-Likelihood: -252.89
No. Observations: 112 AIC: 525.8
Df Residuals: 102 BIC: 553.0
Df Model: 9
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
————
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