*4.1. Bayesian VAR*

First, the focus is on the benchmark model; the Bayesian VAR(3) model is described as follows:

$$y\_t = \beta\_1 y\_{t-1} + \beta\_2 y\_{t-2} + \beta\_3 y\_{t-3} + \epsilon\_t, \quad \epsilon\_t \sim N(0, \Sigma\_{\mathfrak{c}\_t}), \text{ for } t = 1, \dots, T,$$

with *T* the number of total days of the data. Since this model is for every cryptocurrency, the equation above can be rewritten in stacked form:

$$\begin{aligned} \Upsilon\_t &= Z\_t \beta + \epsilon\_t, \quad \beta = \text{vec}(\beta\_1, \beta\_2, \beta\_3), \\ Z\_t &= (I\_N \otimes X\_t), \end{aligned}$$

where *Xt* = [*yt*−1, *yt*−2, *yt*−<sup>3</sup>] , for every cryptocurrency.
