Diagnostics

Chapter Three talks about diagnostics. As in regression analysis, several properties of residuals should be satisfied, if the fitted model is appropriate. Residuals should be a realization of a white or IID sequence. They should have zero as a mean. Their variance, σ‎2, should be constant for all values of the Time variable. They should be normally distributed as well. This chapter explains how to test these points.

Smoothing

Chapter Five explains how to make trends stand out more clearly by reducing residual fluctuations in a time series, focusing on two widely employed techniques, exponential smoothing and moving average smoothing.

Time Series Analysis in the Social Sciences

This chapter explains how time series analysis has been applied in the social sciences.

Time Series Analysis as an Impact Analysis Method

Chapter Seven explains interrupted time series analysis. This chapter includes the impact analysis of the Three-Strikes-Out law with October 1994 (when Public Law 103-322 was enacted) as the intervention point.

Forecasting

Chapter Four explains how to predict future values based on the estimated time series model or with algorithms and how to evaluate the accuracy of the estimated model.

Modeling

Chapter Two defines important concepts and explains the structure of time series data. Then, it explains the univariate time series modeling procedure, such as how to visually inspect a time series; how to transform an original time series when its variance is not constant; how to estimate seasonal patterns and trends; how to obtain residuals; how to estimate the systematic pattern of residuals; and how to test the randomness of residuals.

Time Series Analysis with Two or More Time Series

Chapter Six explains time series analysis with one or more independent variables. The dependent variable is the monthly violent crime rates and the independent variables are unemployment rates and inflation. This chapter discusses several topics related to the robustness of estimated models, such as how to prewhiten a time series, how to deal with trends and seasonal components, how to deal with autoregressive residuals, and how to discern changes of the dependent variable caused by independent variables from its simple continuity. This chapter also discusses the concepts of co-integration and long-memory effect and related topics such as error correction models and autoregressive distributive lags models.