# Writing a VAR(1) with ARCH(1) errors as a bilinear model?

I have been reading a paper and found this quote?

"Note that a linear conditional mean model with ARCH disturbances can be described by a nonlinear specification without ARCH, i.e. the bilinear model."

How would I actually go about writing the bilinear model?

A general bilinear model $$BL(p, q, r, s)$$ can be written as
$$X_t - \sum_j^p \phi_j X_{t-j}=\varepsilon_{t}+\sum_j^p \theta_i \varepsilon_{t-i} + \sum_k^r \sum_{k'}^s b_{k,k'}X_{t-k}\varepsilon_{t-k'}$$
where the sequence of $$\varepsilon$$'s is i.i.d with mean zero and variance $$\sigma^2$$