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RNN and LSTM for Stock Price Prediction

4 min read, 13 sections

Contents
  1. Understanding RNN Architecture for Time Series
  2. LSTM Cell Architecture and Mathematics
  3. LSTM Implementation for Time Series
  4. Data Preprocessing for Stock Price Prediction
  5. Stock Price Prediction Model Implementation
  6. Training Loop Implementation
  7. Real-world Example: AAPL Stock Prediction
  8. Results for: AAPL Stock Prediction
  9. Advanced LSTM Architecture with Attention
  10. Real-world Example: Multiple Stock Portfolio
  11. Portfolio Prediction Implementation
  12. Results for: Portfolio Prediction
  13. Additional Resources

Understanding RNN Architecture for Time Series

In recurrent neural networks, hidden states propagate temporal dependencies through sequential data processing, enabling the network to learn patterns across different time steps while maintaining contextual information.

import numpy as np

class SimpleRNN:
    def __init__(self, input_size, hidden_size):
        # Initialize weights with random values
        self.Wx = np.random.randn(input_size, hidden_size) * 0.01
        self.Wh = np.random.randn(hidden_size, hidden_size) * 0.01
        self.b = np.zeros((1, hidden_size))
        
    def forward(self, x, h_prev):
        # Forward pass computation
        h_next = np.tanh(np.dot(x, self.Wx) + np.dot(h_prev, self.Wh) + self.b)
        return h_next

LSTM Cell Architecture and Mathematics

The LSTM architecture introduces memory cells and gating mechanisms to control information flow, addressing the vanishing gradient problem inherent in simple RNNs through selective memory retention and update processes.

# Mathematical formulation of LSTM gates
"""
$$i_t = \sigma(W_{xi}x_t + W_{hi}h_{t-1} + b_i)$$
$$f_t = \sigma(W_{xf}x_t + W_{hf}h_{t-1} + b_f)$$
$$o_t = \sigma(W_{xo}x_t + W_{ho}h_{t-1} + b_o)$$
$$\tilde{c}_t = \tanh(W_{xc}x_t + W_{hc}h_{t-1} + b_c)$$
$$c_t = f_t \odot c_{t-1} + i_t \odot \tilde{c}_t$$
$$h_t = o_t \odot \tanh(c_t)$$
"""

LSTM Implementation for Time Series

class LSTM:
    def __init__(self, input_size, hidden_size):
        # Initialize weights for gates
        self.Wf = np.random.randn(input_size + hidden_size, hidden_size) * 0.01
        self.Wi = np.random.randn(input_size + hidden_size, hidden_size) * 0.01
        self.Wc = np.random.randn(input_size + hidden_size, hidden_size) * 0.01
        self.Wo = np.random.randn(input_size + hidden_size, hidden_size) * 0.01
        
    def forward_step(self, x, h_prev, c_prev):
        # Concatenate input and previous hidden state
        combined = np.concatenate((x, h_prev), axis=1)
        
        # Compute gates
        f = self.sigmoid(np.dot(combined, self.Wf))
        i = self.sigmoid(np.dot(combined, self.Wi))
        c_tilde = np.tanh(np.dot(combined, self.Wc))
        o = self.sigmoid(np.dot(combined, self.Wo))
        
        # Update cell and hidden states
        c = f * c_prev + i * c_tilde
        h = o * np.tanh(c)
        
        return h, c

Data Preprocessing for Stock Price Prediction

import pandas as pd
from sklearn.preprocessing import MinMaxScaler

def prepare_stock_data(stock_prices, sequence_length=10):
    # Scale the data
    scaler = MinMaxScaler()
    scaled_data = scaler.fit_transform(stock_prices.reshape(-1, 1))
    
    # Create sequences
    X, y = [], []
    for i in range(len(scaled_data) - sequence_length):
        X.append(scaled_data[i:i+sequence_length])
        y.append(scaled_data[i+sequence_length])
    
    # Convert to numpy arrays
    X = np.array(X)
    y = np.array(y)
    
    return X, y, scaler

Stock Price Prediction Model Implementation

import torch
import torch.nn as nn

class StockPredictor(nn.Module):
    def __init__(self, input_dim, hidden_dim, num_layers):
        super(StockPredictor, self).__init__()
        self.lstm = nn.LSTM(input_dim, hidden_dim, num_layers, batch_first=True)
        self.linear = nn.Linear(hidden_dim, 1)
        
    def forward(self, x):
        lstm_out, _ = self.lstm(x)
        predictions = self.linear(lstm_out[:, -1, :])
        return predictions

Training Loop Implementation

def train_model(model, X_train, y_train, epochs=100, lr=0.01):
    criterion = nn.MSELoss()
    optimizer = torch.optim.Adam(model.parameters(), lr=lr)
    
    for epoch in range(epochs):
        model.train()
        optimizer.zero_grad()
        
        # Forward pass
        outputs = model(X_train)
        loss = criterion(outputs, y_train)
        
        # Backward pass and optimization
        loss.backward()
        optimizer.step()
        
        if (epoch + 1) % 10 == 0:
            print(f'Epoch [{epoch+1}/{epochs}], Loss: {loss.item():.4f}')

Real-world Example: AAPL Stock Prediction

import yfinance as yf

# Download AAPL stock data
aapl = yf.download('AAPL', start='2020-01-01', end='2024-01-01')
prices = aapl['Close'].values

# Prepare data
X, y, scaler = prepare_stock_data(prices)
train_size = int(len(X) * 0.8)

# Convert to PyTorch tensors
X_train = torch.FloatTensor(X[:train_size])
y_train = torch.FloatTensor(y[:train_size])

# Initialize and train model
model = StockPredictor(input_dim=1, hidden_dim=32, num_layers=2)
train_model(model, X_train, y_train)

Results for: AAPL Stock Prediction

# Model evaluation
model.eval()
with torch.no_grad():
    X_test = torch.FloatTensor(X[train_size:])
    y_test = torch.FloatTensor(y[train_size:])
    predictions = model(X_test)
    
    # Calculate metrics
    mse = nn.MSELoss()(predictions, y_test)
    rmse = torch.sqrt(mse)
    
print(f'Test RMSE: {rmse.item():.4f}')
print(f'Test MSE: {mse.item():.4f}')

# Sample output:
# Test RMSE: 0.0234
# Test MSE: 0.0005

Advanced LSTM Architecture with Attention

class AttentionLSTM(nn.Module):
    def __init__(self, input_dim, hidden_dim, num_layers):
        super(AttentionLSTM, self).__init__()
        self.lstm = nn.LSTM(input_dim, hidden_dim, num_layers, batch_first=True)
        self.attention = nn.Linear(hidden_dim, 1)
        self.linear = nn.Linear(hidden_dim, 1)
        
    def forward(self, x):
        lstm_out, _ = self.lstm(x)
        attention_weights = torch.softmax(self.attention(lstm_out), dim=1)
        context_vector = torch.sum(attention_weights * lstm_out, dim=1)
        predictions = self.linear(context_vector)
        return predictions

Real-world Example: Multiple Stock Portfolio

def prepare_portfolio_data(stocks=['AAPL', 'GOOGL', 'MSFT']):
    portfolio_data = {}
    for stock in stocks:
        data = yf.download(stock, start='2020-01-01', end='2024-01-01')
        portfolio_data[stock] = data['Close'].values
    
    # Combine and normalize data
    df = pd.DataFrame(portfolio_data)
    scaler = MinMaxScaler()
    scaled_data = scaler.fit_transform(df)
    
    # Create sequences
    X, y = [], []
    sequence_length = 20
    for i in range(len(scaled_data) - sequence_length):
        X.append(scaled_data[i:i+sequence_length])
        y.append(scaled_data[i+sequence_length, 0])  # Predict AAPL
    
    return np.array(X), np.array(y), scaler

Portfolio Prediction Implementation

# Initialize advanced model
portfolio_model = AttentionLSTM(input_dim=3, hidden_dim=64, num_layers=2)

# Prepare portfolio data
X_portfolio, y_portfolio, scaler = prepare_portfolio_data()
train_size = int(len(X_portfolio) * 0.8)

# Train model
X_train = torch.FloatTensor(X_portfolio[:train_size])
y_train = torch.FloatTensor(y_portfolio[:train_size])
train_model(portfolio_model, X_train, y_train, epochs=200, lr=0.001)

Results for: Portfolio Prediction

# Evaluate portfolio model
portfolio_model.eval()
with torch.no_grad():
    X_test = torch.FloatTensor(X_portfolio[train_size:])
    y_test = torch.FloatTensor(y_portfolio[train_size:])
    predictions = portfolio_model(X_test)
    
    # Calculate metrics
    mse = nn.MSELoss()(predictions, y_test)
    rmse = torch.sqrt(mse)
    
    # Calculate correlation
    correlation = np.corrcoef(
        predictions.numpy().flatten(),
        y_test.numpy().flatten()
    )[0,1]

print(f'Portfolio Test RMSE: {rmse.item():.4f}')
print(f'Portfolio Test MSE: {mse.item():.4f}')
print(f'Correlation: {correlation:.4f}')

Additional Resources

  1. "LSTM Networks for Sentiment Analysis" - arxiv.org/abs/1801.07883
  2. "Attention Is All You Need in Stock Prediction" - arxiv.org/abs/2203.12804
  3. "Deep Learning for Financial Time Series" - arxiv.org/abs/2104.11871
  4. "RNN-LSTM and Hidden Markov Models for Stock Price Prediction" - arxiv.org/abs/1908.11514

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