This paper develops a novel hybrid Autoregressive Distributed Lag Mixed Data Sampling (ARDL-MIDAS) model that integrates both deep neural network multi-head attention Transformer mechanisms, and a number of covariates, including sophisticated stochastic text time-series features, into a mixed-frequency time-series regression model with long memory structure. In doing so, we demonstrate how the resulting class of ARDL-MIDAS-Transformer models allows one to maintain the interpretability of the time-series models whilst exploiting the deep neural network attention architectures. The latter may be used for higher-order interaction analysis, or, as in our use case, for design of Instrumental Variables to reduce bias in the estimation of the infinite lag ARDL-MIDAS model. Our approach produces an accurate, interpretable forecasting framework that allows one to forecast end-of-day sentiment intra-daily, with readily attainable time-series regressors. In this regard, we conduct a statistical time-series analysis on mixed data frequencies to discover and study the relationships between sentiment from our custom stochastic text time-series sentiment framework, alternative popular sentiment extraction frameworks (BERT and VADER), and technology factors, as well as to investigate the role that price discovery has on retail cryptocurrency investors’ sentiment (crypto sentiment). This is an interesting time-series modelling challenge as it involves working with time-series regression models in which the time-series response process, and the regression time-series covariates, are observed at different time scales. Specifically, a detailed real-data study is conducted where we explore the relationship between daily crypto market sentiment (of positive, negative and neutral polarity) and the intra-daily (hourly) price log-return dynamics of crypto markets. The sentiment indices constructed for a variety of “topics” and news sources are produced as a collection of time-series capturing the daily sentiment polarity signals for each “topic”, namely each particular market or crypto asset. Different sentiment methods are developed in a time-series context, and utilised in the proposed hybrid regression framework. Furthermore, technology factors are introduced to capture network effects, such as the hash rate which is an important aspect of the money supply relating to the mining of new crypto assets, and block hashing for transaction verification. Throughout our real data study, we provide guidance and insights on how to use our hybrid model to combine—in a transparent, non-black-box way—covariates obtained with different time resolutions, how to understand the arising dynamics between these covariates, potentially under the presence of long memory structure, and, finally, successfully leverage these in forecasting applications. The hybrid model developed demonstrated superior performance to alternatives in both in-sample and forecasting application on real data.
- Text sentiment NLP time-series modelling
- Mixed-data sampling time-series regression (MIDAS)
- Transformer deep neural network
- Natural language processing (NLP)
- Multi-scale resolution data
- Gegenbauer long memory