Introduction, Five Important Practical Problems, Autocorrelation Function and Spectrum of Stationary Processes: Autocorrelation Properties of Stationary Models, Spectral Properties of Stationary Models.

Linear Stationary Models: General Linear Process, Autoregressive Processes, Moving Average Processes, Mixed Autoregressive–Moving Average Processes.

Linear Nonstationary Models: Autoregressive Integrated Moving Average Processes, Three Explicit Forms for the ARIMA Model, Integrated Moving Average Processes.

Forecasting: Minimum Mean Square Error Forecasts and Their Properties, Calculating Forecasts and Probability Limits, Examples of Forecast Functions and Their Updating, Use of State-Space Model Formulation for Exact Forecasting.

Model Identification: Objectives of Identification, Identification Techniques, Initial Estimates for the Parameters, Model Multiplicity.

Parameter Estimation: Study of the Likelihood and Sum-of-Squares Functions, Nonlinear Estimation, Some Estimation Results for Specific Models, Likelihood Function Based on the State-Space Model, Estimation Using Bayes’ Theorem.

Model Diagnostic Checking: Checking the Stochastic Model, Overfitting, Diagnostic Checks Applied to Residuals, Use of Residuals to Modify the Model.

Analysis of Seasonal Time Series: Parsimonious Models for Seasonal Time Series, Some Aspects of More General Seasonal ARIMA Models, Structural Component Models and Deterministic Seasonal Components, Regression Models with Time Series Error Terms.

Multivariate Time Series Analysis: Stationary Multivariate Time Series, Vector Autoregressive Models, Vector Moving Average Models, Vector Autoregressive–Moving Average Models, Forecasting for Vector Autoregressive–Moving Average Processes, State- Space Form of the VARMA Model, Nonstationary and Cointegration