The Multidimensional Relationships between Sentiment, Returns and Volatility

Modern time series analysis is facing the increasing availability of multidimensional data generated over time. In finance, co-movements can be observed, for instance, across different indicators (e.g.\ returns, volatility and sentiment) belonging to the same asset, as well as among indicators observed for different assets. The collection of assets and indicators naturally forms matrix-valued time series observations. Against this, we propose ML and Bayesian estimation of autoregressive models for matrix-valued financial time series. We demonstrate that the model is able to: a) handle multidimensional, and potentially high-dimensional, financial data; b) yield enhanced interpretability and new measures of multidimensional financial connectedness; c) yields enhanced forecasting performances in high-dimensional settings. Properties of the model are demonstrated through a real example to cryptocurrency market data. Our findings reveal only a weak evidence of directional spillover from sentiment indicators to returns and volatility, partly contrasting with the hypothesis that noise traders impact returns or volatility