The chapter discusses the fundamentals and advanced topics of time series analysis, emphasizing the distinction between time series and general multivariate analysis due to the temporal order of observations. It covers the historical development of time series analysis, from early methods like harmonic analysis to modern techniques such as spectral analysis and autoregressive moving-average (ARMA) models. The chapter also delves into the theoretical aspects, including stationarity, ergodicity, and the Wold decomposition, which are crucial for understanding the behavior of time series data. It explores the estimation and inference methods for time series models, the prediction and extraction of unobserved components, and the analysis of multiple time series. Additionally, it addresses the challenges posed by unit roots, co-integration, and long memory processes, as well as the modeling of nonlinear time series. The chapter concludes with applications of time series analysis in economics, such as analyzing cyclic properties, seasonal adjustment, forecasting, and dynamic econometric modeling.The chapter discusses the fundamentals and advanced topics of time series analysis, emphasizing the distinction between time series and general multivariate analysis due to the temporal order of observations. It covers the historical development of time series analysis, from early methods like harmonic analysis to modern techniques such as spectral analysis and autoregressive moving-average (ARMA) models. The chapter also delves into the theoretical aspects, including stationarity, ergodicity, and the Wold decomposition, which are crucial for understanding the behavior of time series data. It explores the estimation and inference methods for time series models, the prediction and extraction of unobserved components, and the analysis of multiple time series. Additionally, it addresses the challenges posed by unit roots, co-integration, and long memory processes, as well as the modeling of nonlinear time series. The chapter concludes with applications of time series analysis in economics, such as analyzing cyclic properties, seasonal adjustment, forecasting, and dynamic econometric modeling.