High dimensional time series data arise in a wide range of disciplines, including finance, signal processing, neuroscience, meteorology, seismology and many other areas. For low dimensional time series there is a well-developed estimation and inference theory. Inference theory in the high dimensional setting has been rarely studied. In this talk, I will give an overview of the work that is proposed to develop and advance statistical inference theory for high dimensional time series data analysis including parameter estimation, construction of simultaneous confidence intervals, prediction, model selection, Granger causality test, hypothesis testing and spectral domain estimation.