Gaussian Mixture Models

Combining supervised and unsupervised learning methods to predict financial market movements ArXiv ID: 2409.03762 “View on arXiv” Authors: Unknown Abstract The decisions traders make to buy or sell an asset depend on various analyses, with expertise required to identify patterns that can be exploited for profit. In this paper we identify novel features extracted from emergent and well-established financial markets using linear models and Gaussian Mixture Models (GMM) with the aim of finding profitable opportunities. We used approximately six months of data consisting of minute candles from the Bitcoin, Pepecoin, and Nasdaq markets to derive and compare the proposed novel features with commonly used ones. These features were extracted based on the previous 59 minutes for each market and used to identify predictions for the hour ahead. We explored the performance of various machine learning strategies, such as Random Forests (RF) and K-Nearest Neighbours (KNN) to classify market movements. A naive random approach to selecting trading decisions was used as a benchmark, with outcomes assumed to be equally likely. We used a temporal cross-validation approach using test sets of 40%, 30% and 20% of total hours to evaluate the learning algorithms’ performances. Our results showed that filtering the time series facilitates algorithms’ generalisation. The GMM filtering approach revealed that the KNN and RF algorithms produced higher average returns than the random algorithm. ...

Gaussian Recombining Split Tree ArXiv ID: 2405.16333 “View on arXiv” Authors: Unknown Abstract Binomial trees are widely used in the financial sector for valuing securities with early exercise characteristics, such as American stock options. However, while effective in many scenarios, pricing options with CRR binomial trees are limited. Major limitations are volatility estimation, constant volatility assumption, subjectivity in parameter choices, and impracticality of instantaneous delta hedging. This paper presents a novel tree: Gaussian Recombining Split Tree (GRST), which is recombining and does not need log-normality or normality market assumption. GRST generates a discrete probability mass function of market data distribution, which approximates a Gaussian distribution with known parameters at any chosen time interval. GRST Mixture builds upon the GRST concept while being flexible to fit a large class of market distributions and when given a 1-D time series data and moments of distributions at each time interval, fits a Gaussian mixture with the same mixture component probabilities applied at each time interval. Gaussian Recombining Split Tre Mixture comprises several GRST tied using Gaussian mixture component probabilities at the first node. Our extensive empirical analysis shows that the option prices from the GRST align closely with the market. ...