However, to put this on more formal ground, we want to work again with the log returns
of the two financial time series. Figure 6-8 shows these graphically:
In [ 79 ]: rets = np.log(data / data.shift( 1 ))
rets.head()
Out[79]: EUROSTOXX VSTOXX
1999-01-04 NaN NaN
1999-01-05 0.017228 0.489248
1999-01-06 0.022138 -0.165317
1999-01-07 -0.015723 0.256337
1999-01-08 -0.003120 0.021570
In [ 80 ]: rets.plot(subplots=True, grid=True, style=‘b’, figsize=( 8 , 6 ))Figure 6-8. Log returns of EURO STOXX 50 and VSTOXX
We have everything together to implement the regression analysis. In what follows, the
EURO STOXX 50 returns are taken as the independent variable while the VSTOXX
returns are taken as the dependent variable:
In [ 81 ]: xdat = rets[‘EUROSTOXX’]
ydat = rets[‘VSTOXX’]
model = pd.ols(y=ydat, x=xdat)
model
Out[81]: ––––––––-Summary of Regression Analysis–––––-
––– Formula: Y ~ <x> + <intercept> Number of Observations: 4033
Number of Degrees of Freedom: 2 R-squared: 0.5322
Adj R-squared: 0.5321 Rmse: 0.0389 F-stat (1, 4031): 4586.3942, p-value: 0.0000 Degrees of Freedom: model 1, resid 4031 –––––––—Summary of Estimated Coefficients–––––
–––
Variable Coef Std Err t-stat p-value CI 2.5%
CI 97.5%
–––––––––––––––––––––––—
–––
x -2.7529 0.0406 -67.72 0.0000 -2.8326
-2.6732