# Do Cryptocurrency Prices Camouflage Latent Economic Effects? A Bayesian Hidden Markov Approach +
## 1 Introduction
Unlike the BTC blockchain, the Ethereum blockchain has been launched eponymously and is governed, or more aptly researched and developed, by the Ethereum Foundation [21], a non-profit organization-based in Switzerland. The architecture of the Ethereum ecosystem has far-reaching implications on its long-term development and sustainability that clearly differentiate it from BTC. Supporting smart contract execution--execution of code snippets that go beyond the simple monetary transactions of BTC--Ethereum has scheduled a transition from the currently computationally heavy Proof of Work (introduced by BTC and followed by most cryptocurrencies) to the computationally efficient alternative of Proof of Stake, which saves on energy resources and provides a scalable infrastructure while retaining the same security guarantees as Proof of Work. Without going further into the technical details, the main motivation to study ETH that stems from these considerations is the following. Given the different technological advancements that are promised by Ethereum, will ETH become independent from BTC and follow its own path as a cryptocurrency or are after all the values of all cryptocurrencies inevitably tied, as they are up to now [16]? Keeping in mind that ETH--i.e., the native coin--is only one of the main applications of the ETH blockchain--and the blockchain technology in general--it should also be noted that price movements of ETH may not necessarily align in the future with technological advancements in the Ethereum blockchain. From a methodological perspective, we perform a two-layer Bayesian analysis. First, we transform the cryptocurrency series into a binary series and apply a logistic regression model on the transformed series. Specifically, if the current price return, i.e., \(Y_{t}-Y_{t-1}\), exceeds a predefined threshold then we assign the value 1 and 0 otherwise. Then, we investigate whether the logistic regression model--which is widely used by applied statisticians and econometricians for analyzing binary data, see [22] and references therein--with a specific covariate set is an appropriate model for estimating the probability of observing the value 1 in these binary series. We use the methodology of [PERSON] et al. [23] to make inference on the model's parameters with an additional reversible jump step to allow for model uncertainty, cf. Section 2.1. Secondly, we model the log-price series data using a novel Hidden Markov (regime switching) model, namely the non-homogeneous Polya Gamma Hidden Markov model (NHPG) of [24], cf. Section 2.2. Hidden Markov models introduce time-variation in the parameters through an underlying unobserved discrete process. In brief, at any given time \(t\), the observed log-price data point depends on a latent (hidden) state. Hence, conditionally on the hidden states, the parameters of the data generating process vary and thus allowing for a flexible data representation. In our setting, the underlying process follows a binomial process with exogenous variables. It has been shown that the NHPG model outperforms similar models in forecasting conventional financial data, cf. [25]. Also, it uses Bayesian Model Averaging (BMA) approach for inference which has been shown to possess desirable properties for forecasting applications [26; 27; 28; 29]. With all these in mind, the questions we aim to address are the following:  
1. Does the underlying information from fiat currencies, commodities, stock indices and blockchain specific variables explain/predict the probability of positive returns? 2. Do the same variables have explanatory/predictive power on both the BTC and ETH cryptocurrencies? 3. Do the same explanatory variables affect the BTC price series both on the long and short run? We use daily data (for both the response and the explanatory variables) between 2017 and 2019. For question Q3, we compare the BTC data of the whole 2014-2019 period to the 2017-2019 period (also used in Q1-Q2).