APPLYING NONLINEAR TIME SERIES ANALYSIS TO PSYCHOLOGICAL DATA

Abstract

Nonlinear and time-varying systems are ubiquitous, exhibiting interesting properties and posing major challenges for research. They are relatively understudied in psychology due to the predominance of general linear models. This thesis examines the viability of nonlinear time-series analysis methods for use with longitudinal psychological data. In particular, it compares the performance of nonlinear time-series analysis (NLTSA) with linear time autoregressive integrated moving average (ARIMA) models, by applying these methods to make forecasts on simulated datasets, employing prediction accuracy as a measure of goodness of fit. To determine their relative performance on psychological data, prediction accuracies are tested as the level of noise and length of dataset are varied. The prediction accuracies are also compared on a dataset from a psychopathology study. NLTSA outperforms ARIMA on nonlinear non-chaotic systems whenever noise levels are low to moderate, but is outperformed by ARIMA on a linear system across all conditions. Increasing dataset length has little effect on the prediction accuracy of either method for all nonlinear systems, but improves both methods’ accuracy for the linear system. Both methods exhibit poor prediction accuracy for chaotic systems in all conditions. The results support the use of NLTSA on longitudinal psychological data, with certain caveats.