Stock Price Prediction Using Random Forests (R-squared problem)

Question

    #===========================Importing packages=================================
import yfinance as yf
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestRegressor
import matplotlib.pyplot as plt
import seaborn as sns
import pandas_ta as ta
from sklearn.metrics import accuracy_score, precision_score, recall_score, f1_score
from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score
from xgboost import XGBRegressor
from sklearn.model_selection import GridSearchCV
from lightgbm import LGBMRegressor
import math

#=========================Data collection======================================
# Fetch historical stock data for NVIDIA, from yahoo finance
symbol = 'NVDA'
start_date = '2021-12-01'
end_date = '2023-12-01'
stock_data = yf.download(symbol, start=start_date, end=end_date)

#========================Exploratory data analysis=============================
# Display the first few rows of the dataset
print("Head of the dataset:")
print(stock_data.head())

# Summary statistics
print("\nSummary statistics:")
print(stock_data.describe())

# Check for missing values
print("\nMissing values:")
print(stock_data.isnull().sum())

# Visualize the distribution of 'Adj Close' prices
plt.figure(figsize=(12, 6))
sns.histplot(stock_data['Adj Close'], bins=50, kde=True)
plt.title('Distribution of Adj Close Prices')
plt.xlabel('Adj Close Price')
plt.ylabel('Frequency')
plt.show()

# Visualize the adj closing prices over time
plt.figure(figsize=(14, 6))
plt.plot(stock_data.index, stock_data['Adj Close'], label='Adj Close Price', color='blue')
plt.title('Adj Closing Prices Over Time')
plt.xlabel('Date')
plt.ylabel('Adj Close Price')
plt.legend()
plt.show()

# Visualize the daily returns
plt.figure(figsize=(14, 6))
plt.plot(stock_data.index, stock_data['Adj Close'].pct_change(), label='Daily Returns', color='green')
plt.title('Daily Returns Over Time')
plt.xlabel('Date')
plt.ylabel('Daily Returns')
plt.legend()
plt.show()

#==========================Create features & target============================
stock_data['SMA_50'] = stock_data['Adj Close'].rolling(window=50).mean()
stock_data['SMA_200'] = stock_data['Adj Close'].rolling(window=200).mean()
stock_data['Daily_Return'] = stock_data['Adj Close'].pct_change()
stock_data['RSI'] = stock_data.ta.rsi(close='Adj Close', length=14, append=True)
stock_data['EMA'] = stock_data.ta.ema(close='Adj Close', length=9, append=True)

stock_data = stock_data.dropna()

# Define features and target variable
features = ['Open', 'RSI']
target = 'Adj Close'

# Extract features and target
X = stock_data[features]
y = stock_data[target]

# Display the first few rows of the dataset with features and target
print(stock_data[features + [target]].head())

#========================Creating X and y======================================
# Split the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1)

# Overwrite the test set
X_test = X.tail(math.floor(0.2 * len(stock_data))) 
y_test = y.tail(math.floor(0.2 * len(stock_data)))
# We will use these for all three seperate ML methdos

#=============================Random Forest====================================
# Define the hyperparameter grid, for hyperparameter tuning
rf_param_grid = {
    'n_estimators': [50, 100, 200],
    'max_depth': [2, 5, 10],
    'min_samples_split': [2, 5, 10],
    'min_samples_leaf': [1, 2, 4]
}

# Create a Random Forest Regressor
rf_model = RandomForestRegressor(random_state=1)

# Initialize GridSearchCV
grid_search = GridSearchCV(estimator=rf_model, param_grid=rf_param_grid, cv=3, scoring='neg_mean_squared_error', n_jobs=-1)

# Perform grid search to find the best hyperparameters
grid_search.fit(X_train, y_train)

# Get the best hyperparameters
rf_best_params = grid_search.best_params_

# Create and train the Random Forest model with the best hyperparameters
best_rf_model = RandomForestRegressor(random_state=1, **rf_best_params)
best_rf_model.fit(X_train, y_train)

# Predict the stock prices on the test set using the tuned model
rf_predictions = best_rf_model.predict(X_test)

# Evaluate the model using regression metrics
rf_mae = mean_absolute_error(y_test, rf_predictions)
rf_mse = mean_squared_error(y_test, rf_predictions)
rf_r2 = r2_score(y_test, rf_predictions)
rf_mape = np.mean(np.abs((y_test - rf_predictions) / y_test)) * 100
rf_rmse = np.sqrt(rf_mse)

print(f"Mean Absolute Error (MAE): {rf_mae:.2f}")
print(f"Mean Squared Error (MSE): {rf_mse:.2f}")
print(f"R-squared (R2): {rf_r2:.2f}")
print(f"Root Mean Squared Error (RMSE): {rf_rmse:.2f}")
print(f"Mean Absolute Percentage Error (MAPE): {rf_mape:.2f}%")
for param, value in rf_best_params.items():
    print(f"{param}: {value}")
    
# Plot the actual vs predicted prices
plt.figure(figsize=(12, 6))
plt.plot(stock_data.index[-len(y_test):], y_test, label='Actual Prices', color='blue')
plt.plot(stock_data.index[-len(y_test):], rf_predictions, label='Predicted Prices', color='red')
plt.title(f'{symbol} Stock Price Prediction using Random Forest')
plt.xlabel('Date')
plt.ylabel('Stock Price')
plt.legend()
plt.show()

# Get feature importances from the Random Forest model
rf_feature_importances = best_rf_model.feature_importances_

# Create a DataFrame to store feature names and their importances
rf_feature_importance_df = pd.DataFrame({'Feature': features, 'Importance': rf_feature_importances})

# Sort the DataFrame by importance in descending order
rf_feature_importance_df = rf_feature_importance_df.sort_values(by='Importance', ascending=False)

# Plot the feature importance
plt.figure(figsize=(10, 6))
sns.barplot(x='Importance', y='Feature', data=rf_feature_importance_df, palette='viridis')
plt.title('Random Forest - Feature Importance')
plt.show()

I have some trouble running this code. Whenever running the code with different feautures ('Open', 'RSI'), the model always returns a R-squared of 1. Which would likely mean we are overfitting the model, how can we solve this or is this normal with stock price prediction?

Answer 1

Given this model is predicting the closing price using the opening price and RSI as features - the high R-Squared does indicate that the model is adept at predicting the closing price based on values of the opening price and RSI in the test set.

However, if there were suddenly a random shock - such as a stock price opening at an expected range but then there was a sudden dip/climb in price - then this model would be rendered ineffective.

Putting aside this model for a moment - attempting to predict future stock prices in the first instance is fraught with error. The reason is that stock price is a stochastic time series - i.e. there is a high degree of inherent randomness in the time series which makes prediction very difficult.

Let's consider the issue for seasonality as one example. Here is a time series with a defined seasonal lag of 7 days, which can then be used for predictive purposes with a forecasting model such as ARIMA.

Now, let's have a look at the autocorrelation for the adjusted closing price in your example.

We observe a high degree of autocorrelation across lags but no inherent seasonal pattern. However, this strong correlation between lags doesn't always hold - a sudden change in stock price would render any previous correlations irrelevant.

Therefore, the model looks like it has predictive power on paper, which is evidenced by a low RMSE of 4.94 relative to the mean value of 450.04 in the test set. However, the model is in effect predicting past values of itself (given that opening price is normally quite close to that of closing) - predictive error is likely to increase greatly when this is not the case.

Depending on what your goal is, you might consider a probability-based model to determine value at risk, such as a Monte Carlo simulation. This involves calculating the daily returns for the stock and then generating a simulation based on the mean and standard deviation. The aim of this would not be to predict future prices per se, but rather to analyse what could be the expected return, as well as expected maximum downside/upside.

Disclaimer: None of the above is meant as investment or financial advice of any sort. The answer is simply intended to discuss the application of data science principles given the data posed in the question.