Hypothesis Testing

Investor Sentiment and Market Movements: A Granger Causality Perspective ArXiv ID: 2510.15915 “View on arXiv” Authors: Tamoghna Mukherjee Abstract The stock market is heavily influenced by investor sentiment, which can drive buying or selling behavior. Sentiment analysis helps in gauging the overall sentiment of market participants towards a particular stock or the market as a whole. Positive sentiment often leads to increased buying activity and vice versa. Granger causality can be applied to ascertain whether changes in sentiment precede changes in stock prices.The study is focused on this aspect and tries to understand the relationship between close price index and sentiment score with the help of Granger causality inference. The study finds a positive response through hypothesis testing. ...

How to verify that a given process is a Lévy-Driven Ornstein-Uhlenbeck Process ArXiv ID: 2501.03434 “View on arXiv” Authors: Unknown Abstract Assuming that a Lévy-Driven Ornstein-Uhlenbeck (or CAR(1)) processes is observed at discrete times $0$, $h$, $2h$,$\cdots$ $[“T/h”]h$. We introduce a step-by-step methodological approach on how a person would verify the model assumptions. The methodology involves estimating the model parameters and approximating the driving process. We demonstrate how to use the increments of the approximated driving process, along with the estimated parameters, to test the assumptions that the CAR(1) process is Lévy-driven. We then show how to test the hypothesis that the CAR(1) process belongs to a specified class of Lévy processes. The performance of the tests is illustrated through multiple simulations. Finally, we demonstrate how to apply the methodology step-by-step to a variety of economic and financial data examples. ...

Contrastive Learning of Asset Embeddings from Financial Time Series ArXiv ID: 2407.18645 “View on arXiv” Authors: Unknown Abstract Representation learning has emerged as a powerful paradigm for extracting valuable latent features from complex, high-dimensional data. In financial domains, learning informative representations for assets can be used for tasks like sector classification, and risk management. However, the complex and stochastic nature of financial markets poses unique challenges. We propose a novel contrastive learning framework to generate asset embeddings from financial time series data. Our approach leverages the similarity of asset returns over many subwindows to generate informative positive and negative samples, using a statistical sampling strategy based on hypothesis testing to address the noisy nature of financial data. We explore various contrastive loss functions that capture the relationships between assets in different ways to learn a discriminative representation space. Experiments on real-world datasets demonstrate the effectiveness of the learned asset embeddings on benchmark industry classification and portfolio optimization tasks. In each case our novel approaches significantly outperform existing baselines highlighting the potential for contrastive learning to capture meaningful and actionable relationships in financial data. ...

High-Dimensional Mean-Variance Spanning Tests ArXiv ID: 2403.17127 “View on arXiv” Authors: Unknown Abstract We introduce a new framework for the mean-variance spanning (MVS) hypothesis testing. The procedure can be applied to any test-asset dimension and only requires stationary asset returns and the number of benchmark assets to be smaller than the number of time periods. It involves individually testing moment conditions using a robust Student-t statistic based on the batch-mean method and combining the p-values using the Cauchy combination test. Simulations demonstrate the superior performance of the test compared to state-of-the-art approaches. For the empirical application, we look at the problem of domestic versus international diversification in equities. We find that the advantages of diversification are influenced by economic conditions and exhibit cross-country variation. We also highlight that the rejection of the MVS hypothesis originates from the potential to reduce variance within the domestic global minimum-variance portfolio. ...