A Tutorial and Methodological Review of Linear Time Series Models: Using R and SPSS

Abstract

This article introduces autoregressive (AR) linear models to psychology students and researchers through a step-by-step approach using SPSS and R. Despite their relevance, AR models remain underutilized in behavioral sciences, possibly due to conceptual challenges and difficulties interpreting autocorrelation and seasonality. Our aim is to simplify their implementation by presenting time series models as special cases of linear regression, using accessible language and practical examples. The article illustrates AR estimation using real data, incorporating lagged values as predictors of the dependent variable. Residual diagnostics, a frequently overlooked aspect in applied research, receive special attention, including figures and statistical tests. As Kmenta (1971) demonstrated, serially correlated residuals can lead to artificially low p values for the parameter estimates, potentially resulting in explanatory variables being deemed significant when they truly are not. To promote understanding, we offer intuitive visualizations and clear decision rules for model building, lag selection, and seasonality detection. We compare polynomial and AR models using the confounding test. The data set and annotated R and SPSS scripts are included to support replication and help readers learn basic syntax. We also discuss conceptual and practical limitations of moving average, integration (I), and exponential smoothing models, emphasizing the practical advantages of AR-only models in psychological contexts. Throughout, we stress the importance of aligning statistical models with theoretical assumptions and the temporal structure of data. By combining step-by-step explanations, visual guidance, and real-data applications, this tutorial provides a practical foundation for incorporating AR models into applied psychological research.