We consider a multivariate time series model which represents a high
dimensional vector process as a sum of three terms: a linear regression of some
observed regressors, a linear combination of some latent and serially
correlated factors, and a vector white noise. We investigate the inference
without imposing stationary conditions on the target multivariate time series,
the regressors and the underlying factors. Furthermore we deal with the
endogeneity that there exist correlations between the observed regressors and
the unobserved factors. We also consider the model with nonlinear regression
term which can be approximated by a linear regression function with a large
number of regressors. The convergence rates for the estimators of regression
coefficients, the number of factors, factor loading space and factors are
established under the settings when the dimension of time series and the number
of regressors may both tend to infinity together with the sample size. The
proposed method is illustrated with both simulated and real data examples
