Forecasting Apple Stock Prices with Deep Convolutional Neural Networks

Introduction

Predicting the future prices of stocks is a notoriously difficult yet alluring problem. With the potential for significant financial gain, stock price forecasting has attracted interest from investors, traders, and researchers alike. However, stock prices are influenced by a multitude of interrelated factors, from a company‘s financial health to overall market conditions to investors‘ future expectations. This complexity makes it extremely challenging to anticipate the movement of stock prices with a high degree of accuracy.

In recent years, the field of deep learning has made remarkable progress in tackling complex problems by learning patterns and representations from data. Deep learning techniques have achieved state-of-the-art results across a range of domains, including computer vision, natural language processing, and time series forecasting. In particular, convolutional neural networks (CNNs) have shown great promise in learning local patterns and extracting meaningful features from grid-like data structures.

While CNNs have been most widely applied to 2D image data, an emerging area of research explores their use in modeling and forecasting 1D sequence data such as time series. By treating the time series as a 1D grid and applying convolutions along the temporal dimension, CNNs can capture local temporal dependencies and learn useful representations for forecasting.

In this article, we will investigate the application of deep convolutional neural networks to forecast the stock price of Apple Inc. (AAPL). As one of the largest and most widely traded companies in the world, Apple‘s stock price is of great interest to investors and a common target for forecasting efforts. We will walk through the process of building a CNN model in Python using the TensorFlow deep learning library. Through this hands-on example, we aim to illustrate the potential and key considerations of using deep CNNs for stock price forecasting.

Dataset

For this analysis, we will use historical price data for Apple stock (AAPL). Yahoo! Finance provides easy access to historical stock prices through their API. Using the yfinance Python package, we can retrieve the past prices programmatically:

!pip install yfinance
import yfinance as yf

aapl = yf.download(‘AAPL‘, start=‘2010-01-01‘, end=‘2022-12-31‘)

This retrieves the daily prices for AAPL from January 1, 2010 to December 31, 2022. The data includes the opening, high, low, and closing prices as well as the trading volume for each trading day. For our model, we will focus on forecasting the daily closing prices.

We can visualize the historical closing prices to get a sense of the overall trajectory and variability:

import matplotlib.pyplot as plt

plt.figure(figsize=(10,4))
plt.plot(aapl[‘Close‘])
plt.title(‘AAPL Stock Price History‘)
plt.xlabel(‘Date‘) 
plt.ylabel(‘Closing Price (USD)‘)
plt.show()

The plot shows the significant appreciation of Apple‘s stock price over the past decade, although with some substantial fluctuations along the way. Our goal will be to train a deep learning model to forecast the future daily closing prices based on a historical lookback window.

Data Preparation

Before we can train a CNN model on the Apple price data, we need to transform it into a suitable input format. CNNs require the input data to have a grid-like structure where proximity in the grid has meaning. We can treat our time series price data as a 1D grid, where proximity corresponds to temporal locality.

To prepare the data, we will:

1. Normalize the price data to put it on a consistent scale
2. Create rolling lookback windows of a fixed size to use as model inputs
3. Split the data into training and testing sets

Here‘s the code to perform these steps:

from sklearn.preprocessing import MinMaxScaler

# Normalize the prices to [0,1] range
scaler = MinMaxScaler()
prices = aapl[‘Close‘].values.reshape(-1,1) 
scaled_prices = scaler.fit_transform(prices)

lookback = 60  # Use past 60 days of prices as input

# Create rolling lookback windows 
X, y = [], []
for i in range(lookback, len(scaled_prices)):
    X.append(scaled_prices[i-lookback:i])
    y.append(scaled_prices[i])
X, y = np.array(X), np.array(y)

# Train/test split (use last year for testing)
split = -365 
X_train, X_test = X[:split], X[split:] 
y_train, y_test = y[:split], y[split:]

print(X_train.shape, X_test.shape)

After running this, we have X_train and X_test arrays with shape (number of samples, lookback, 1) ready to feed into the CNN model. The corresponding y_train and y_test contain the next day‘s price that we want to forecast.

Building the CNN Model

With the data prepared, we can now design and train the CNN forecasting model. We will use Keras, the high-level deep learning API packaged with TensorFlow.

The key aspects in designing the CNN architecture are:

1. Stacking multiple convolutional layers to extract hierarchical features
2. Using 1D convolutions since the input is a 1D sequence
3. Flattening the final convolutional output to feed into dense layers
4. Incorporating a look-ahead mechanism to forecast multiple steps ahead

Here‘s the code defining the CNN architecture:

from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense, Conv1D, Flatten

model = Sequential()
model.add(Conv1D(filters=64, kernel_size=3, activation=‘relu‘, input_shape=(lookback,1)))
model.add(Conv1D(filters=32, kernel_size=3, activation=‘relu‘))
model.add(Flatten())
model.add(Dense(64, activation=‘relu‘))
model.add(Dense(1))

model.compile(optimizer=‘adam‘, loss=‘mse‘)

This architecture has two 1D convolutional layers to extract local temporal patterns, followed by flattening and two dense layers to output the forecasted price.

To train the model:

history = model.fit(X_train, y_train, 
                    epochs=100, 
                    batch_size=32,
                    validation_data=(X_test, y_test),
                    verbose=1)

After training, we can evaluate the model‘s performance on the test set:

from sklearn.metrics import mean_squared_error

y_pred = model.predict(X_test)

mse = mean_squared_error(y_test, y_pred)
print(f‘Test MSE: {mse:.4f}‘)

We can also visualize the model‘s predictions against the actual prices:

y_pred = scaler.inverse_transform(y_pred) 
y_test = scaler.inverse_transform(y_test)

plt.figure(figsize=(10,4))
plt.plot(y_test, label=‘Actual‘)
plt.plot(y_pred, label=‘Predicted‘)
plt.title(‘Apple Stock Price Forecasts‘)
plt.xlabel(‘Time‘)
plt.ylabel(‘Price (USD)‘)
plt.legend()
plt.show()

The plot compares the actual prices over the test period to the prices forecasted by the trained CNN model.

Discussion and Limitations

The CNN approach shows some promise in capturing the high-level trends and overall direction of Apple‘s stock price. However, there are clear limitations and potential improvements to discuss.

First, the CNN model is only using the past price history to make forecasts, ignoring the multitude of other factors that drive stock prices. Incorporating additional relevant data like trading volume, news sentiment, or overall market indices could provide a more holistic view and potentially improve predictions.

Second, the model is only forecasting the next day‘s closing price based on a fixed input window. In practice, we may want to forecast further into the future or have a more flexible input size. Techniques such as sequence-to-sequence models or dilated convolutions could help address these issues.

Additionally, it‘s important to recognize that our testing setup optimistically assumes we have the full history up to the day before we want to forecast. In reality, we would need to evaluate the model on a more realistic rolling basis, using only data that would have been available at each forecasted time step.

Finally, any stock forecasting model is inherently limited by the semi-random, noisy nature of stock price movements. Even a model that performs well on historical data is not guaranteed to be profitable in live trading. It‘s crucial to continuously monitor and validate any forecasting model on new data.

Conclusion

In this article, we explored the application of deep convolutional neural networks to forecasting stock prices, focusing on predicting Apple (AAPL) stock‘s future price based on its historical price data. We walked through the process of retrieving and preparing the price data, designing and training a CNN architecture in Python with TensorFlow, and evaluating the model‘s performance.

The CNN-based approach demonstrated some ability to learn meaningful temporal patterns and forecast the overall direction of Apple‘s stock price. However, there are clear limitations and areas for improvement, such as incorporating additional data sources, modifying the architecture for longer-range forecasts, and evaluating on a rolling basis.

Ultimately, stock price forecasting remains a highly challenging problem, and any results should be taken with a grain of salt. Deep learning methods like CNNs offer a promising avenue to extract complex patterns from price histories, but models must be continuously validated and improved. As research into applying deep learning to stock forecasting advances, it will be exciting to see what new insights and innovations emerge.