advanced-algorithmic-trading

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At this stage we have the necessary data to begin creating a set of statistical machine learning
models.
Validation Set Approach
Now that we have the financial data we need to create a set of predictive regression models we
can use the above cross-validation methods to obtain estimates for the test error.
The first task is to import the models from Scikit-Learn. We will choose a linear regression
model with polynomial features. This provides us with the ability to choose varying degrees
of flexibility simply by increasing the degree of the features’ polynomial order. Initially we are
going to consider the validation set approach to cross validation.
Scikit-Learn provides a validation set approach via the train_test_split method found
in the cross_validation module. We will also need to import the KFold method for k-fold
cross validation later, as well as the linear regression model itself. We need to import the MSE
calculation as well as Pipeline and PolynomialFeatures. The latter two allow us to easily
create a set of polynomial feature linear regression models with minimal additional coding:
..
from sklearn.cross_validation import train_test_split, KFold
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import PolynomialFeatures
..
Once the modules are imported we can create a Pandas DataFrame that uses ten of the prior
lagging days of Amazon returns as predictors. We can then create ten separate random splittings
of the data into a training and validation set.
Finally, for multiple degrees of the polynomial features of the linear regression, we can calculate
the test error. This provides us with ten separate test error curves, each value of which
shows the test MSE for a differing degree of polynomial kernel:
..
..
def validation_set_poly(random_seeds, degrees, X, y):
"""
Use the train_test_split method to create a
training set and a validation set (50% in each)
using "random_seeds" separate random samplings over
linear regression models of varying flexibility
"""
sample_dict = dict(
[("seed_%s" % i,[]) for i in range(1, random_seeds+1)]
)
# Loop over each random splitting into a train-test split
for i in range(1, random_seeds+1):
print("Random: %s" % i)