# Can VARMA handle non-linear data?

I know that traditional ARIMA models cannot handle non-linear data but I was unable to find any place where it states whether if VARMA can handle non-linear data or only linear. Please clarify this for me.

VARMA is just a multivariate counterpart of ARMA, just like VAR is a multivariate counterpart of AR. All of these models are linear in parameters. A VARMA(p,q) model postulates that a multivariate time series $$y_t$$ (a vector) is a linear function of its own past values $$y_{t-l}$$ for $$l=1,\dots,p$$ and past values of the error vector $$\varepsilon_{t-m}$$ for $$m=1,\dots,q$$: $$y_t = \sum_{l=1}^p \Phi_l y_{t-l} + \sum_{m=1}^q \Theta_m \varepsilon_{t-m} + \varepsilon_t.$$ ($$\Phi_l$$ and $$\Theta_m$$ are square matrices.) In this sense, VARMA is as linear as ARMA (or VAR, or AR).