Principal Component Analysis (PCA)

News Sentiment Embeddings for Stock Price Forecasting ArXiv ID: 2507.01970 “View on arXiv” Authors: Ayaan Qayyum Abstract This paper will discuss how headline data can be used to predict stock prices. The stock price in question is the SPDR S&P 500 ETF Trust, also known as SPY that tracks the performance of the largest 500 publicly traded corporations in the United States. A key focus is to use news headlines from the Wall Street Journal (WSJ) to predict the movement of stock prices on a daily timescale with OpenAI-based text embedding models used to create vector encodings of each headline with principal component analysis (PCA) to exact the key features. The challenge of this work is to capture the time-dependent and time-independent, nuanced impacts of news on stock prices while handling potential lag effects and market noise. Financial and economic data were collected to improve model performance; such sources include the U.S. Dollar Index (DXY) and Treasury Interest Yields. Over 390 machine-learning inference models were trained. The preliminary results show that headline data embeddings greatly benefit stock price prediction by at least 40% compared to training and optimizing a machine learning system without headline data embeddings. ...

Generalized Factor Neural Network Model for High-dimensional Regression ArXiv ID: 2502.11310 “View on arXiv” Authors: Unknown Abstract We tackle the challenges of modeling high-dimensional data sets, particularly those with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships. Our approach enables a seamless integration of concepts from non-parametric regression, factor models, and neural networks for high-dimensional regression. Our approach introduces PCA and Soft PCA layers, which can be embedded at any stage of a neural network architecture, allowing the model to alternate between factor modeling and non-linear transformations. This flexibility makes our method especially effective for processing hierarchical compositional data. We explore ours and other techniques for imposing low-rank structures on neural networks and examine how architectural design impacts model performance. The effectiveness of our method is demonstrated through simulation studies, as well as applications to forecasting future price movements of equity ETF indices and nowcasting with macroeconomic data. ...

A Random Forest approach to detect and identify Unlawful Insider Trading ArXiv ID: 2411.13564 “View on arXiv” Authors: Unknown Abstract According to The Exchange Act, 1934 unlawful insider trading is the abuse of access to privileged corporate information. While a blurred line between “routine” the “opportunistic” insider trading exists, detection of strategies that insiders mold to maneuver fair market prices to their advantage is an uphill battle for hand-engineered approaches. In the context of detailed high-dimensional financial and trade data that are structurally built by multiple covariates, in this study, we explore, implement and provide detailed comparison to the existing study (Deng et al. (2019)) and independently implement automated end-to-end state-of-art methods by integrating principal component analysis to the random forest (PCA-RF) followed by a standalone random forest (RF) with 320 and 3984 randomly selected, semi-manually labeled and normalized transactions from multiple industry. The settings successfully uncover latent structures and detect unlawful insider trading. Among the multiple scenarios, our best-performing model accurately classified 96.43 percent of transactions. Among all transactions the models find 95.47 lawful as lawful and $98.00$ unlawful as unlawful percent. Besides, the model makes very few mistakes in classifying lawful as unlawful by missing only 2.00 percent. In addition to the classification task, model generated Gini Impurity based features ranking, our analysis show ownership and governance related features based on permutation values play important roles. In summary, a simple yet powerful automated end-to-end method relieves labor-intensive activities to redirect resources to enhance rule-making and tracking the uncaptured unlawful insider trading transactions. We emphasize that developed financial and trading features are capable of uncovering fraudulent behaviors. ...

When can weak latent factors be statistically inferred? ArXiv ID: 2407.03616 “View on arXiv” Authors: Unknown Abstract This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal factor strength relative to the noise level or signal-to-noise ratio. Our theory is applicable regardless of the relative growth rate between the cross-sectional dimension $N$ and temporal dimension $T$. This more realistic assumption and noticeable result require completely new technical device, as the commonly-used leave-one-out trick is no longer applicable to the case with cross-sectional dependence. Another notable advancement of our theory is on PCA inference $ - $ for example, under the regime where $N\asymp T$, we show that the asymptotic normality for the PCA-based estimator holds as long as the signal-to-noise ratio (SNR) grows faster than a polynomial rate of $\log N$. This finding significantly surpasses prior work that required a polynomial rate of $N$. Our theory is entirely non-asymptotic, offering finite-sample characterizations for both the estimation error and the uncertainty level of statistical inference. A notable technical innovation is our closed-form first-order approximation of PCA-based estimator, which paves the way for various statistical tests. Furthermore, we apply our theories to design easy-to-implement statistics for validating whether given factors fall in the linear spans of unknown latent factors, testing structural breaks in the factor loadings for an individual unit, checking whether two units have the same risk exposures, and constructing confidence intervals for systematic risks. Our empirical studies uncover insightful correlations between our test results and economic cycles. ...

Principal Component Analysis and Hidden Markov Model for Forecasting Stock Returns ArXiv ID: 2307.00459 “View on arXiv” Authors: Unknown Abstract This paper presents a method for predicting stock returns using principal component analysis (PCA) and the hidden Markov model (HMM) and tests the results of trading stocks based on this approach. Principal component analysis is applied to the covariance matrix of stock returns for companies listed in the S&P 500 index, and interpreting principal components as factor returns, we apply the HMM model on them. Then we use the transition probability matrix and state conditional means to forecast the factors returns. Reverting the factor returns forecasts to stock returns using eigenvectors, we obtain forecasts for the stock returns. We find that, with the right hyperparameters, our model yields a strategy that outperforms the buy-and-hold strategy in terms of the annualized Sharpe ratio. ...