Using the latest advancements in AI to predict stock market movements

       In this notebook I will create a complete process for predicting stock price movements. Follow along and we will achieve some pretty good results. For that purpose we will use a Generative Adversarial Network (GAN) with LSTM, a type of Recurrent Neural Network, as generator, and a Convolutional Neural Network, CNN, as a discriminator. We use LSTM for the obvious reason that we are trying to predict time series data. Why we use GAN and specifically CNN as a discriminator? That is a good question: there are special sections on that later.

       We will go into greater details for each step, of course, but the most difficult part is the GAN: very tricky part of successfully training a GAN is getting the right set of hyperparameters. For that reason we will use Bayesian optimisation (along with Gaussian processes) and Reinforcement learning (RL) for deciding when and how to change the GAN's hyperparameters (the exploration vs. exploitation dilemma). In creating the reinforcement learning we will use the most recent advancements in the field, such as Rainbow and PPO.

       We will use a lot of different types of input data. Along with the stock's historical trading data and technical indicators, we will use the newest advancements in NLP (using 'Bidirectional Embedding Representations from Transformers', BERT, sort of a transfer learning for NLP) to create sentiment analysis (as a source for fundamental analysis), Fourier transforms for extracting overall trend directions, Stacked autoencoders for identifying other high-level features, Eigen portfolios for finding correlated assets, autoregressive integrated moving average (ARIMA) for the stock function approximation, and many more, in order to capture as much information, patterns, dependencies, etc, as possible about the stock. As we all know, the more (data) the merrier. Predicting stock price movements is an extremely complex task, so the more we know about the stock (from different perspectives) the higher our changes are.

       For the purpose of creating all neural nets we will use MXNet and its high-level API - Gluon, and train them on multiple GPUs.

Note: Although I try to get into details of the math and the mechanisms behind almost all algorithms and techniques, this notebook is not explicitly intended to explain how machine/deep learning, or the stock markets, work. The purpose is rather to show how we can use different techniques and algorithms for the purpose of accurately predicting stock price movements, and to also give rationale behind the reason and usefulness of using each technique at each step.

Notebook created: January 9, 2019.

Figure 1 - The overall architecture of our work

<center><img src='imgs/main.jpg' width=1060></img></center>

Table of content

• Introduction
• Acknowledgement
• The data
  • Correlated assets
  • Technical indicators
  • Fundamental analysis
    • Bidirectional Embedding Representations from Transformers - BERT
  • Fourier transforms for trend analysis
  • ARIMA as a feature
  • Statistical checks
    • Heteroskedasticity, multicollinearity, serial correlation
  • Feature Engineering
    • Feature importance with XGBoost
  • Extracting high-level features with Stacked Autoencoders
    • Activation function - GELU (Gaussian Error)
    • Eigen portfolio with PCA
  • Deep Unsupervised Learning for anomaly detection in derivatives pricing
• Generative Adversarial Network - GAN
  • Why GAN for stock market prediction?
  • Metropolis-Hastings GAN and Wasserstein GAN
  • The Generator - One layer RNN
    • LSTM or GRU
    • The LSTM architecture
    • Learning rate scheduler
    • How to prevent overfitting and the bias-variance trade-off
    • Custom weights initializers and custom loss metric
  • The Discriminator - 1D CNN
    • Why CNN as a discriminator?
    • The CNN architecture
  • Hyperparameters
• Hyperparameters optimization
  • Reinforcement learning for hyperparameters optimization
    • Theory
      • Rainbow
      • PPO
    • Further work on Reinforcement learning
  • Bayesian optimization
    • Gaussian process
• The result
• What is next?
• Disclaimer

1. Introduction <a class="anchor" id="overview"></a>

       Accurately predicting the stock markets is a complex task as there are millions of events and pre-conditions for a particilar stock to move in a particular direction. So we need to be able to capture as many of these pre-conditions as possible. We also need make several important assumptions: 1) markets are not 100% random, 2) history repeats, 3) markets follow people's rational behavior, and 4) the markets are 'perfect'. And, please, do read the Disclaimer at the <a href="#disclaimer">bottom</a>.

       We will try to predict the price movements of Goldman Sachs (NYSE: GS). For the purpose, we will use daily closing price from January 1st, 2010 to December 31st, 2018 (seven years for training purposes and two years for validation purposes). We will use the terms 'Goldman Sachs' and 'GS' interchangeably.

2. Acknowledgement <a class="anchor" id="acknowledgement"></a>

       Before we continue, I'd like to thank my friends <a href="https://github.com/manganganath">Nuwan</a> and <a href="https://github.com/Q4living">Thomas</a> without whose ideas and support I wouldn't have been able to create this work.

3. The Data <a class="anchor" id="thedata"></a>

       We need to understand what affects whether GS's stock price will move up or down. It is what people as a whole think. Hence, we need to incorporate as much information (depicting the stock from different aspects and angles) as possible. (We will use daily data - 1,585 days to train the various algorithms (70% of the data we have) and predict the next 680 days (test data). Then we will compare the predicted results with a test (hold-out) data. Each type of data (we will refer to it as feature) is explained in greater detail in later sections, but, as a high level overview, the features we will use are:

1. Correlated assets - these are other assets (any type, not necessarily stocks, such as commodities, FX, indices, or even fixed income securities). A big company, such as Goldman Sachs, obviously doesn't 'live' in an isolated world - it depends on, and interacts with, many external factors, including its competitors, clients, the global economy, the geo-political situation, fiscal and monetary policies, access to capital, etc. The details are listed later.
2. Technical indicators - a lot of investors follow technical indicators. We will include the most popular indicators as independent features. Among them - 7 and 21 days moving average, exponential moving average, momentum, Bollinger bands, MACD.
3. Fundamental analysis - A very important feature indicating whether a stock might move up or down. There are two features that can be used in fundamental analysis: 1) Analysing the company performance using 10-K and 10-Q reports, analysing ROE and P/E, etc (we will not use this), and 2) News - potentially news can indicate upcoming events that can potentially move the stock in certain direction. We will read all daily news for Goldman Sachs and extract whether the total sentiment about Goldman Sachs on that day is positive, neutral, or negative (as a score from 0 to 1). As many investors closely read the news and make investment decisions based (partially of course) on news, there is a somewhat high chance that if, say, the news for Goldman Sachs today are extremely positive the stock will surge tomorrow. One crucial point, we will perform feature importance (meaning how indicative it is for the movement of GS) on absolutely every feature (including this one) later on and decide whether we will use it. More on that later.<br/>        For the purpose of creating accurate sentiment prediction we will use Neural Language Processing (NLP). We will use BERT - Google's recently announced NLP approach for transfer learning for sentiment classification stock news sentiment extraction.
4. Fourier transforms - Along with the daily closing price, we will create Fourier transforms in order to generalize several long- and short-term trends. Using these transforms we will eliminate a lot of noise (random walks) and create approximations of the real stock movement. Having trend approximations can help the LSTM network pick its prediction trends more accurately.
5. Autoregressive Integrated Moving Average (ARIMA) - This was one of the most popular techniques for predicting future values of time series data (in the pre-neural networks ages). Let's add it and see if it comes off as an important predictive feature.
6. Stacked autoencoders - most of the afore