CFTM: Continuous time fractional topic model

In this paper, we propose the Continuous Time Fractional Topic Model (cFTM), a new method for dynamic topic modeling. This approach incorporates fractional Brownian motion~(fBm) to effectively identify positive or negative correlations in topic and word distribution over time, revealing long-term dependency or roughness. Our theoretical analysis shows that the cFTM can capture these long-term dependency or roughness in both topic and word distributions, mirroring the main characteristics of fBm. Moreover, we prove that the parameter estimation process for the cFTM is on par with that of LDA, traditional topic models. To demonstrate the cFTM's property, we conduct empirical study using economic news articles. The results from these tests support the model's ability to identify and track long-term dependency or roughness in topics over time.

Uncertainty Aware Trader-Company Method: Interpretable Stock Price Prediction Capturing Uncertainty

Machine learning is an increasingly popular tool with some success in predicting stock prices. One promising method is the Trader-Company~(TC) method, which takes into account the dynamism of the stock market and has both high predictive power and interpretability. Machine learning-based stock prediction methods including the TC method have been concentrating on point prediction. However, point prediction in the absence of uncertainty estimates lacks credibility quantification and raises concerns about safety. The challenge in this paper is to make an investment strategy that combines high predictive power and the ability to quantify uncertainty. We propose a novel approach called Uncertainty Aware Trader-Company Method~(UTC) method. The core idea of this approach is to combine the strengths of both frameworks by merging the TC method with the probabilistic modeling, which provides probabilistic predictions and uncertainty estimations. We expect this to retain the predictive power and interpretability of the TC method while capturing the uncertainty. We theoretically prove that the proposed method estimates the posterior variance and does not introduce additional biases from the original TC method. We conduct a comprehensive evaluation of our approach based on the synthetic and real market datasets. We confirm with synthetic data that the UTC method can detect situations where the uncertainty increases and the prediction is difficult. We also confirmed that the UTC method can detect abrupt changes in data generating distributions. We demonstrate with real market data that the UTC method can achieve higher returns and lower risks than baselines.