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# Cracking The Code: Predicting S&P 500 Returns With CatBoost

### CatBoost’s Magic Wand: Predicting S&P 500 Returns with Confidence

Machine learning algorithms are numerous. Many are useful in predicting time series data. This article explores an ensemble learning model called CatBoost and shows how to use it to predict the returns of the S&P 500 index.

### Introduction to CatBoost

CatBoost, or “Categorical Boosting,” is a robust open-source gradient boosting library developed by Yandex for machine learning tasks, particularly regression and classification.

It’s distinguished by its ability to efficiently handle categorical features, a common challenge in real-world datasets, without requiring extensive preprocessing. CatBoost employs innovative techniques like target encoding and ordered boosting for this purpose. Notably, it excels in preventing overfitting through a combination of strategies like ordered boosting and depth-first search, making it a reliable choice for generalization.

Despite its capabilities, CatBoost remains fast in terms of training, often outperforming other gradient boosting implementations. Additionally, CatBoost provides tools for model interpretability, aiding in the understanding and explanation of feature importance, further enhancing its appeal for both beginners and experienced professionals in the field.

### Predicting S&P 500 Returns Using CatBoost

The main aim of this article is to write a Python code that uses CatBoost to predict the returns of the S&P 500 index using its lagged returns.

The plan of attack is as follows:

Import the S&P 500 prices into Python.

Split the data into training and testing.

Fit the model to the training data and predict on the test data. The features used are the last 50 returns of the index.

Evaluate the mode using a simple hit ratio and chart the predicted values.

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Use the following code to create the algorithm:

```
import numpy as np
from catboost import CatBoostRegressor
import matplotlib.pyplot as plt
import pandas_datareader as pdr
def data_preprocessing(data, num_lags, train_test_split):
# Prepare the data for training
x = []
y = []
for i in range(len(data) - num_lags):
x.append(data[i:i + num_lags])
y.append(data[i+ num_lags])
# Convert the data to numpy arrays
x = np.array(x)
y = np.array(y)
# Split the data into training and testing sets
split_index = int(train_test_split * len(x))
x_train = x[:split_index]
y_train = y[:split_index]
x_test = x[split_index:]
y_test = y[split_index:]
return x_train, y_train, x_test, y_test
start_date = '1960-01-01'
end_date = '2023-09-01'
# Set the time index if it's not already set
data = (pdr.get_data_fred('SP500', start = start_date, end = end_date).dropna())
# Perform differencing to make the data stationary
data_diff = data.diff().dropna()
data_diff = np.reshape(np.array(data_diff), (-1))
x_train, y_train, x_test, y_test = data_preprocessing(data_diff, 50, 0.95)
# Create a CatBoostRegressor model
model = CatBoostRegressor(iterations = 100, learning_rate = 0.1, depth = 6, loss_function = 'RMSE')
# Fit the model to the data
model.fit(x_train, y_train)
# Predict on the same data used for training
y_pred = model.predict(x_test) # Use X, not X_new for prediction
# Plot the original sine wave and the predicted values
plt.plot(y_pred, label='Predicted Data', linestyle='--')
plt.plot(y_test, label='True Data')
plt.legend()
plt.grid()
# Calculating the Hit Ratio
same_sign_count = np.sum(np.sign(y_pred) == np.sign(y_test)) / len(y_test) * 100
print('Hit Ratio = ', same_sign_count, '%')
```

The following Figure shows a comparison between true and predicted data.

The output of the code is as follows:

`Hit Ratio = 59.01639344262295 %`

It seems like the algorithm does a not so bad job at predicting the returns. Still, this needs more investigation and research.

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