Abstract: We obtain an invariance principle for non-stationary vector-valued stochastic processes. It is shown that, under mild conditions, the partial sums of non-stationary processes can be approximated on a richer probability space by sums of independent Gaussian random vectors with nearly optimal bounds. The latter Gaussian approximation result has a wide range of applications in the study of multiple non-stationary time series.
Key words and phrases: Central limit theorem, functional linear models, Gaussian approximation, local stationarity, non-stationary nonlinear multiple time series.