Random forests use bootstrapping, which helps address variance issues. However, traditional bootstrapping assumes the data is stationary and independent—assumptions that don’t hold for stock market data, which is inherently non-stationary and time-dependent.
The Problem with Standard Bootstrapping
Think of bootstrapping as creating multiple alternative market histories. Unfortunately, simple bootstrapping randomly samples from the same market, breaking the sequential structure of financial data.
The Solution: Block Bootstrapping
Block bootstrapping preserves temporal dependencies by sampling contiguous blocks of data rather than individual points. This helps random forests generalize better when applied to financial data.
How to Use It
To see if this improves your investment model, you could integrate block bootstrapping into a grid search cross-validation for Random Forests.
Here’s a Python implementation of a Random Forest with Block Bootstrapping, which runs as-is:
import numpy as np
import pandas as pd
from sklearn.ensemble import RandomForestRegressor
from sklearn.metrics import mean_squared_error
from sklearn.model_selection import train_test_split
def block_bootstrap(X, y, block_size=10, n_samples=None):
"""
Perform block bootstrapping on time-series data.
Parameters:
- X: Feature matrix (pandas DataFrame or numpy array)
- y: Target variable (pandas Series or numpy array)
- block_size: Size of each bootstrap block
- n_samples: Number of total samples to generate (default is len(y))
Returns:
- X_boot: Bootstrapped feature matrix
- y_boot: Bootstrapped target variable
"""
if n_samples is None:
n_samples = len(y)
num_blocks = len(y) // block_size
block_indices = np.arange(num_blocks)
chosen_blocks = np.random.choice(block_indices, size=(n_samples // block_size), replace=True)
X_boot = np.vstack([X[i * block_size:(i + 1) * block_size] for i in chosen_blocks])
y_boot = np.hstack([y[i * block_size:(i + 1) * block_size] for i in chosen_blocks])
return X_boot, y_boot
# Simulated stock data (Replace this with real stock features)
np.random.seed(42)
n_samples = 500 # Total data points (e.g., 500 trading days)
X = np.random.randn(n_samples, 5) # 5 Features (e.g., technical indicators)
y = np.random.randn(n_samples) # Target (e.g., stock returns)
# Perform block bootstrapping
X_boot, y_boot = block_bootstrap(X, y, block_size=10)
# Split bootstrapped data into train/test sets
X_train, X_test, y_train, y_test = train_test_split(X_boot, y_boot, test_size=0.2, shuffle=False)
# Train Random Forest model
rf = RandomForestRegressor(n_estimators=100, random_state=42)
rf.fit(X_train, y_train)
# Predictions & performance
y_pred = rf.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
print(f"Mean Squared Error: {mse:.4f}")