Stochastic simulations with perfectly correlated shocks


in my model I have two exogenous variables:
z_t=(1-\phi) \mu+\phi z_{t-1}+e_t

where e_t is an exogenous shock. My issue is that the exogenous Normal shock e_t has different volatility for the two exogenous processes. The volatility of the first process is \lambda, the second is \sigma. If I want to compute the IRFs with respect to a shock on e, how can I impose different volatilities for the two processes in the shocks block? Is there a better way to do this? I tried to define two different but perfectly correlated shocks, but then the correlation matrix becomes singular. Thanks a lot in advance for any help

You could use
\begin{align}m_t&=-\delta-z_{t-1}-\lambda e_t;\\ z_t&=(1-\phi) \mu+\phi z_{t-1}+\sigma e_t \end{align}


var e=1;
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Thanks a lot, all clear :slight_smile: