Time series models are widely used in fields such as econometrics, finance, biostatistics, industrial metrology, and others. This book mainly studies the theoretical properties and practical applications of complex time series, including the statistical inference of the distribution function of time series, functional time series, and multi-step forward prediction intervals for locally stationary time series. This book can be used as an elective textbook for undergraduates or graduate students majoring in statistics, data science, and related fields. It can also be used as a reference book for statistical researchers, business managers, and government staff to learn forecasting methods.