This course introduces some advanced time series topics beyond the stationary ARMA models and techniques which are relevant in time series applications in the big data era. Our focus will be on non-stationary and nonlinear time series analyses from a nonparametric statistical perspective. Topics include: the concept of unit root and cointegrated processes; unit root testing; ARCH/GARCH models for stochastic volatility; kernel regression; nonparametric smoothing in the time/state domain; nonparametric spectral density estimation; linear and nonlinear state-space models. Some associated computational skills in real data applications will be introduced as well.