AI For Trading: Exercise regression with two stocks (22)

Regression

Install packages

import sys
!{sys.executable} -m pip install -r requirements.txt

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import pandas as pd
import numpy as np
import os
import helper
import quiz_tests
import matplotlib.pyplot as plt

plt.style.use('ggplot')
plt.rcParams['figure.figsize'] = (14, 8)

Simulate two stock prices

# just set the seed for the random number generator
np.random.seed(100)
# use returns to create a price series
drift = 100
r0 = pd.Series(np.random.normal(0, 1, 1000))

s0 = pd.Series(np.cumsum(r0), name='s0') + drift

noise1 = np.random.normal(0, 0.4, 1000)
drift1 = 50
r1 = r0 + noise1
s1 = pd.Series(np.cumsum(r1), name='s1') + drift1

noise2 = np.random.normal(0, 0.4, 1000)
drift2 = 60
r2 = r0 + noise2
s2 = pd.Series(np.cumsum(r2), name='s2') + drift2

pd.concat([s1, s2], axis=1).plot(figsize=(15,6))
plt.show()

## Plot data with scatterplot
sc = plt.scatter(s2, s1, s=30, edgecolor='b', alpha=0.7)
plt.xlabel('s2')
plt.ylabel('s1');

from sklearn.linear_model import LinearRegression

Quiz: Linear Regression

Note that the LinearRegression().fit() expects 2D numpy arrays. Since s1 and s2 are pandas series, we can use Series.values to get the values as a numpy array. Since these are 1D arrays, we can use numpy.reshape(-1,1) to make these 1000 row by 1 column 2 dimensional arrays.

The coefficients of the linear regression, \(\beta\) and intercept for the regression line:
\(y = \beta \times x + intercept\)
Can be obtained after fitting to the data. Use LinearRegression.coef_ for the slope (beta coefficients) and LinearRegression.intercept_ for the intercept. You may want to practice accessing these outside of the function definition, to see if you'll need additional brackets [] to access the values.

def regression_slope_and_intercept(xSeries, ySeries):
    """
    xSeries: pandas series, x variable
    ySeries: pandas series, y variable
    """
    lr = LinearRegression()
    #TODO: get the values from each series, reshape to be 2 dimensional
    #set s1 to the x variable, s2 to the y variable
    xVar = xSeries.values.reshape(-1,1)
    yVar = ySeries.values.reshape(-1,1)

    #TODO: call LinearRegression.fit().  Pass in the x variable then y variable
    lr.fit(xVar,yVar);

    #TODO: obtain the slope and intercept
    slope = lr.coef_[0][0]
    intercept = lr.intercept_[0]

    return (slope, intercept)

quiz_tests.test_regression_slope_and_intercept(regression_slope_and_intercept);

Tests Passed

slope, intercept = regression_slope_and_intercept(s1,s2);
print(f"slope {slope:.2f} and intercept {intercept:.2f}")

slope 0.74 and intercept 30.62

Plot the fitted regression line over the scatterplot

plt.scatter(s2, s1, s=30, edgecolor='b', alpha=0.5);
x = np.linspace(s1.min()-5, s1.max()+5, 2)
yPred = slope * x + intercept
plt.plot(yPred,x, alpha=0.2, lw=3, color='r')
plt.xlabel('s2')
plt.ylabel('s1');

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