A Deep Learning Model to Predict Equity Price Movement

The goal of this project was to make consistent short-term predictions within the equity market with a higher win rate than standard buy-and-hold strategies. After months of work, I have achieved this goal, with all of my additional work moving the goal post of earning more consistent short-term profits. The model uses a PyTorch LSTM neural network to learn from the large dataset that I have collected (~250k datapoints), preprocessed using scikit-learn's StandardScaler class. All my data has been sourced through free or inexpensive market APIs and web scraping techniques, mainly Python's BeautifulSoup library and hidden XHR APIs.

The data that I have found to have the most predictive power is unusual options flow (exceptionally high call or put volume relative to a given company's average), SEC insider trading data, the RSI momentum signal, and news sentiment analysis. For the news sentiment analysis, I have scraped hundreds of thousands of headlines from major market news publications such as Bloomberg, Marketwatch, and Barrons, and have ran them through a pre-trained news sentiment analysis LSTM sourced from Hugging Face to produce a "sentimental" output in the range (-1,1). As of writing this, my model is quite good at predicting when a stock will go up, but not so great at predicting negative movement. When the model outputs a >0.65 probability that the stock will go up, it is approximately 78% accurate (these results were obtained from an independent evaluation set, the training validation set reached over 90% accuracy under these same constraints).

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What is Fourier Analysis?

Fourier analysis is a field of mathematics dedicated to the study of decomposition of arbitrary functions into simple trigonometric sums. The work of Joseph Fourier proves that any twice differentiable periodic function may be expanded into a series of sines and cosines. Fourier analysis is useful for the solution of many differential equations, such as the wave and heat equations, as well as providing elegant proofs for problems in number theory.

The fourier transform is also essential to the topic of fourier analysis. The fourier transform is an operation that maps a function to its "frequency domain," which has many applications for signal processing.

My Research

For this project I reviewed literature of Fourier Analysis methods in finance. Most of my time was spent to determine whether the fast fourier transform (fft) algorithm could be used to discover periodic patterns within market data. To do this, I wrote up some python code that imports closing price data of a given asset over the past ~2000 trading days. I then fit the data with an exponential regression and subtracted it to analyze fluctuations about the asset's natural growth. Finally, I ran the data through the fft, plotting the frequency domain to a pdf file, as well as printing the frequencies with the largest amplitude in the terminal. After running several different assets through my code, it was clear that my method was not especially useful. A significant shortcoming was my limited access to market data, having only been able to import closing prices. Access to higher frequency data would have produced better short term results. To view a presentation of my analysis, click "Read More" below.

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Relaxation Algorithms

A relaxation algorithm is a computational method of solving Laplace's equation in 2 dimensions or higher. Laplace's equation states that the sum of the second order partial derivatives of a given function are equal to zero. This equation is particularly useful in the study of electrostatics and fluid dynamics. The problem with Laplace's equation is that there are no general solutions unless boundary conditions are specified, and analytic solutions prove to be difficult even with trivial boundary conditions. The study of relaxation algorithms allows for the speedy approximation of non-trivial boundary problems.

My Research

My research focused on the application of Laplace's equation to potential theory of electrostatics. I set up a two dimensional lattice that may be initialized on the boundary, then had each internal point update m times according to the "relaxation" procedure. In the case of a two dimensional lattice, this procedure is simply that each node on the lattice is equal to the average of its 4 cartesianally adjacent nodes. I then solved analytically for an arbitrary (and trivial) boundary condition to compare graphical results with that of my algorithm. After verifying the validity of my code, I was able produce graphical results of non-trivial boundaries, such as sinusoids. Click "Read more" to view an in-depth paper of my analysis.

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