Intensive longitudinal measurement designs prominent in econometrics, engineering, biophysics and brain imaging are also quickly coming to the forefront in psychology. Vector autoregressive models (VARs), often in combination with Granger causality testing, are often used in statistical analysis of time series data. Granger causality testing is used to establish the network of effective dynamic connections underlying the data. Yet, for each given data set there exist different versions of VARs that are statistically equivalent (i.e., yield exactly the same fit to the data and are related to each other by smooth transformations). It is shown that these equivalent versions are based on distinct assumptions and yield different results in Granger causality testing. This problem has not been integrally addressed before in the published literature concerned. However, this dependence of Granger causality testing on which equivalent version of the VAR model is selected constitutes a crucial weakness.
The basic question addressed in this project therefore can be summarized as follows: How can one decide which particular element from the set of equivalent VARs is appropriate in each application? This question has not been addressed before in the published literature. The approach developed in this project involves the introduction of a new so-called hybrid VAR that (a) integrates the different equivalent versions of VARs into a single model, (b) enables implementation of powerful statistical tools to determine the appropriate equivalent version for each given time series, and (c) yields unique and valid solutions to Granger causality testing.
