Publication Library
Comparative Analysis of the Hidden Markov Model and LSTM - A Simulative Approach
Description: Time series and sequential data have gained significant attention recently since many real-world processes in various domains such as finance, education, biology, and engineering can be modeled as time series. Although many algorithms and methods such as the Kalman filter, hidden Markov model, and long short term memory (LSTM) are proposed to make inferences and predictions for the data, their usage significantly depends on the application, type of the problem, available data, and sufficient accuracy or loss. In this paper, we compare the supervised and unsupervised hidden Markov model to LSTM in terms of the amount of data needed for training, complexity, and forecasting accuracy. Moreover, we propose various techniques to discretize the observations and convert the problem to a discrete hidden Markov model under stationary and non-stationary situations. Our results indicate that even an unsupervised hidden Markov model can outperform LSTM when a massive amount of labeled data is not available. Furthermore, we show that the hidden Markov model can still be an effective method to process the sequence data even when the first-order Markov assumption is not satisfied.
Created At: 20 April 2025
Updated At: 20 April 2025
Comparative Study of Machine Learning Models for Stock Price Prediction
Description: In this work, we apply machine learning techniques to historical stock prices to forecast future prices. To achieve this, we use recursive approaches that are appropriate for handling time series data. In particular, we apply a linear Kalman filter and different varieties of long short-term memory (LSTM) architectures to historical stock prices over a 10-year range (1/1/2011 - 1/1/2021). We quantify the results of these models by computing the error of the predicted values versus the historical values of each stock. We find that of the algorithms we investigated, a simple linear Kalman filter can predict the next-day value of stocks with low-volatility (e.g., Microsoft) surprisingly well. However, in the case of high-volatility stocks (e.g., Tesla) the more complex LSTM algorithms significantly outperform the Kalman filter. Our results show that we can classify different types of stocks and then train an LSTM for each stock type. This method could be used to automate portfolio generation for a target return rate.
Created At: 20 April 2025
Updated At: 20 April 2025
Neural Augmented Kalman Filtering with Bollinger Bands for Pairs Trading
Description: Pairs trading is a family of trading techniques that determine their policies based on monitoring the relationships between pairs of assets. A common pairs trading approach relies on describing the pair-wise relationship as a linear Space State (SS) model with Gaussian noise. This representation facilitates extracting financial indicators with low complexity and latency using a Kalman Filter (KF), that are then processed using classic policies such as Bollinger Bands (BB). However, such SS models are inherently approximated and mismatched, often degrading the revenue. In this work, we propose KalmenNet-aided Bollinger bands Pairs Trading (KBPT), a deep learning aided policy that augments the operation of KF-aided BB trading. KBPT is designed by formulating an extended SS model for pairs trading that approximates their relationship as holding partial co-integration. This SS model is utilized by a trading policy that augments KF-BB trading with a dedicated neural network based on the KalmanNet architecture. The resulting KBPT is trained in a two-stage manner which first tunes the tracking algorithm in an unsupervised manner independently of the trading task, followed by its adaptation to track the financial indicators to maximize revenue while approximating BB with a differentiable mapping. KBPT thus leverages data to overcome the approximated nature of the SS model, converting the KF-BB policy into a trainable model. We empirically demonstrate that our proposed KBPT systematically yields improved revenue compared with model-based and data-driven benchmarks over various different assets.
Created At: 20 April 2025
Updated At: 20 April 2025
Portfolio Transformer for Attention-Based Asset Allocation
Description: Traditional approaches to financial asset allocation start with returns forecasting followed by an optimization stage that decides the optimal asset weights. Any errors made during the forecasting step reduce the accuracy of the asset weightings, and hence the profitability of the overall portfolio. The Portfolio Transformer (PT) network, introduced here, circumvents the need to predict asset returns and instead directly optimizes the Sharpe ratio, a risk-adjusted performance metric widely used in practice. The PT is a novel end-to-end portfolio optimization framework, inspired by the numerous successes of attention mechanisms in natural language processing. With its full encoder-decoder architecture, specialized time encoding layers, and gating components, the PT has a high capacity to learn long-term dependencies among portfolio assets and hence can adapt more quickly to changing market conditions such as the COVID-19 pandemic. To demonstrate its robustness, the PT is compared against other algorithms, including the current LSTM-based state of the art, on three different datasets, with results showing that it offers the best risk-adjusted performance.
Created At: 20 April 2025
Updated At: 20 April 2025
Axial-LOB - High-Frequency Trading with Axial Attention
Description: Previous attempts to predict stock price from limit order book (LOB) data are mostly based on deep convolutional neural networks. Although convolutions offer efficiency by restricting their operations to local interactions, it is at the cost of potentially missing out on the detection of long-range dependencies. Recent studies address this problem by employing additional recurrent or attention layers that increase computational complexity. In this work, we propose Axial-LOB, a novel fully-attentional deep learning architecture for predicting price movements of stocks from LOB data. By utilizing gated position-sensitive axial attention layers our architecture is able to construct feature maps that incorporate global interactions, while significantly reducing the size of the parameter space. Unlike previous works, Axial-LOB does not rely on hand-crafted convolutional kernels and hence has stable performance under input permutations and the capacity to incorporate additional LOB features. The effectiveness of Axial-LOB is demonstrated on a large benchmark dataset, containing time series representations of millions of high-frequency trading events, where our model establishes a new state of the art, achieving an excellent directional classification performance at all tested prediction horizons.
Created At: 20 April 2025
Updated At: 20 April 2025