  We consider the multilinear polynomial-form process
  \[X(n)=\sum_{1\le i_1<\ldots<i_k<\infty}a_{i_1}\ldots
a_{i_k}\epsilon_{n-i_1}\ldots\epsilon_{n-i_k},\] obtained by applying a
multilinear polynomial-form filter to i.i.d.\ sequence $\{\epsilon_i\}$ where
$\{a_i\}$ is regularly varying. The resulting sequence $\{X(n)\}$ will then
display either short or long memory. Now consider a vector of such X(n), whose
components are defined through different $\{a_i\}$'s, that is, through
different multilinear polynomial-form filters, but using the same
$\{\epsilon_i\}$. What is the limit of the normalized partial sums of the
vector? We show that the resulting limit is either a) a multivariate Gaussian
process with Brownian motion as marginals, or b) a multivariate Hermite
process, or c) a mixture of the two. We also identify the independent
components of the limit vectors.
