Vector autoregressions (VARs) are important statistical tools for empirical analysis.

I develop a statistical framework where multiple economic shocks can affect the

location, scale and shape of the entire conditional distribution of the multiple time series

of the responses, while in the constant coefficient VAR models shocks only affect

the location. To achieve this goal, the multiple dynamic time-series data-generating

process with the parameters being affine functions of random variables is introduced.

Furthermore, I introduce the novel vector quantile autoregression (VQAR) that relates

the vector of autoregressive quantile processes to its lagged values and propose

a procedure for identifying the structural quantile shocks, the type of shock that occurs

with a certain probability. I introduce the quantile impulse response functions

(QIRFs) as a main device for estimating the impact and transmission of the structural

quantile shocks. Asymptotic properties are discussed and bootstrap procedures

are introduced for the inference purposes.