An Introduction to ARIMA and Harmonic Regression Time Series Analysis Methods

A number of data analysis methods fall under the general heading of “time series analysis.” A "time series" refers in general to a set of observations of an individual person; an organization; a community; or any other entity or system across time. Time series methods are well suited for studying how a single system changes across time. For example, a long time series may be “interrupted” by an intervention and then the pre-intervention times series segment can be compared with the time series observations obtained during, and after, the intervention to study the effects of the intervention on the system.

In this workshop participants will learn to use and synthesize two methods of time series analysis, autoregressive integrated moving average (or ARIMA) methods and harmonic regression analysis methods, into a powerful general approach to analyzing time series data. Participants will first be introduced to the concept of autocorrelation in time series data, its causes, effects, and how it can be identified and modeled. Participants will learn to use SPSS to generate autocorrelation and partial autocorrelation plots and how to use these plots to identify various forms of autocorrelation in a time series. Participants will then learn how to model various forms of autocorrelation and then test the adequacy of these models. Methods for testing the effects of interventions will then be presented. These ARIMA methods will be exemplified by an illustrative analysis of data from a study of the implementation of an intervention called Aggression Replacement Training in a short-term shelter for adolescents.

Participants will then be shown how to add harmonic regression analysis methods to the ARIMA methods. In harmonic regression analysis, sine and cosine terms are used to model cycles, or periodicities, in time series data. The use of the periodogram and spectral density plots to identify cycles of different frequencies will be covered. The use of these methods, integrated with the ARIMA methods, will be illustrated by further analysis of the data from the Aggression Replacement Training study.

Finally, methods for testing the effects of an intervention on periodicities in time series data will be added to the ARIMA and harmonic regression methods. Participants will learn how to model various forms of intervention effects, including changes in mean level, changes in cycles or periodicities associated with an intervention, and interaction effects.

At the conclusion of this workshop participants can expect to have a basic understanding of ARIMA and harmonic regression time series analysis methods; of how to test the effects of an intervention on a time series; and how to use SPSS to conduct these analyses.