This chapter introduces the Bayesian approach. We define the key concepts that are needed to understand Bayesian inference and the comparison with frequentist inference. We show how these concepts can be applied in the linear time series models considered earlier and discuss the modern treatment of vector autoregression models from a Bayesian perspective.

This chapter considers the multivariate case, extending the univariate concepts to the vector time series case. We consider vector autoregressions from different points of view.

This chapter introduces the class of autoregressive moving average models and discusses their properties in special cases and in general. We provide alternative methods for the estimation of unknown parameters and describe the properties of the estimators. We discuss key issues like hypothesis testing and model selection.

This chapter is concerned with different approaches to accounting for trend and seasonal components. We consider both deterministic and stochastic approaches and show the overlap and contrast between these approaches. Estimation and inference are treated.

This chapter introduces the frequency-domain view and how this way of thinking can help with understanding periodic behavior and cycles. We define the spectral density function and how commonly used filters affect the spectral shape. We discuss estimation by the periodogram and smoothing methods.

In this chapter we consider the continuous-time setting. We consider some classical models and their estimation, and the more recent literature on high-frequency econometrics.

In this chapter we consider the question of forecasting. We consider model-based and ad hoc approaches to this question. We discuss the issue of forecast evaluation and comparison.

This chapter introduces the state space model and shows how this can be adapted to represent a wide variety of models of use in economics and finance. We define the Kalman filter and show how it can be implemented in leading examples.

This chapter introduces more formal concepts like stationarity and mixing, and explains why they are needed. We also define the autocorrelation function and describe its properties and how it is estimated from sample data. We discuss the properties of the estimator of the mean and autocorrelation, and how they can be used to conduct statistical inference.

This chapter focuses on inference methods under different scenarios with an emphasis on the most general case. We introduce different methods based on smoothing methods, the self-normalization approach, and different types of bootstrap.

This chapter introduces what a time series is and defines the important decomposition into trend, seasonal, and cycle that guides our thinking. We introduce a number of datasets used in the book and plot them to show their key features in terms of these components.