Least squares estimator asymptotics for vector autoregressions with deterministic regressors

We consider a mixed vector autoregressive model with deterministic exogenous regressors and an autoregressive matrix that has characteristic roots inside the unit circle. The errors are $(2+\epsilon)$-integrable martingale differences with heterogeneous second-order conditional moments. The behavior of the ordinary least squares (OLS) estimator depends on the rate of growth of the exogenous regressors. For bounded or slowly growing regressors we prove asymptotic normality. In case of quickly growing regressors (e.g., polynomial trends) the result is negative: the OLS asymptotics cannot be derived using the conventional scheme and any diagonal normalizer.