The basic regression model for the time series data \boldsymbol{y}=(y_1,y_2,...,y_n)^T is

\boldsymbol{y} \sim~ N(X\boldsymbol{b}, \boldsymbol{\Sigma})

with the design matrix X=(\boldsymbol{1}, \boldsymbol{x}_1, ..., \boldsymbol{x}_k), the corresponding regression coefficients \boldsymbol{b}=(b_0, b_1, ..., b_k)^T and the residual variance-variance matrix \Sigma. The k predictors, vectors \boldsymbol{x}_1, ..., \boldsymbol{x}_k, have the same length of n as the response variable \boldsymbol{y}.

Can the model be implemented in `brms`

if I want to impose a prior distribution on the regression coefficients (except b_0): b_i \sim N(b, \tau^2) (i=1,2,...,k)? Also, how to specify the autoregressive structure of the residuals with a band matrix \Sigma?