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X = amzn[["Lag1", "Lag2", "Lag3"]]
y = amzn["Today"]
X = scale(X)
y = scale(y)
The data is split into a training set and a test set, with 70% of the data forming the training
data and the remaining 30% performing the test set. Once again, note that financial time series
data is serially correlated, so this procedure will introduce some error by not accounting for it,
however it serves the purpose for comparison across procedures in this chapter:
# Use the training-testing split with 70% of data in the
# training data with the remaining 30% of data in the testing
X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size=0.3, random_state=random_state
)
The following NumPy arrays store the number of estimators at each axis step, as well as the
actual associated MSE for each of the three ensemble methods. They are all initially set to zero
and are filled in subsequently:
# Pre-create the arrays which will contain the MSE for
# each particular ensemble method
estimators = np.zeros(axis_step)
bagging_mse = np.zeros(axis_step)
rf_mse = np.zeros(axis_step)
boosting_mse = np.zeros(axis_step)
The first ensemble method to be utilised is the bagging procedure. The code iterates over
the total number of estimators (1-1000 in this case, with a step-size of 10), defines the ensemble
model with the correct base model (in this case a regression tree), fits it to the training data
and then calculates the Mean Squared Error on the test data. This MSE is then added to the
bagging MSE array:
# Estimate the Bagging MSE over the full number
# of estimators, across a step size ("step_factor")
for i in range(0, axis_step):
print("Bagging Estimator: %d of %d..." % (
step_factor*(i+1), n_estimators)
)
bagging = BaggingRegressor(
DecisionTreeRegressor(),
n_estimators=step_factor*(i+1),
n_jobs=n_jobs,
random_state=random_state
)
bagging.fit(X_train, y_train)
mse = mean_squared_error(y_test, bagging.predict(X_test))
estimators[i] = step_factor*(i+1)
bagging_mse[i] = mse