We develop a new time series model to investigate the dynamic interactions between the nucleus accumbens and the hippocampus during an associative learning experiment. Preliminary analyses indicated that the spectral properties of the local field potentials at these two regions changed over the trials of the experiment. While many models already take into account nonstationarity within a single trial, the evolution of the dynamics across trials is often ignored. Our proposed model, the slowly evolving locally stationary process (SEv-LSP), is designed to capture nonstationarity both within a trial and across trials. We rigorously define the evolving evolutionary spectral density matrix, which we estimate using a two-stage procedure. In the first stage, we compute the within-trial time-localized periodogram matrix. In the second stage, we develop a data-driven approach that combines information from trial-specific local periodogram matrices. Through simulation studies, we show the utility of our proposed method for analyzing time series data with different evolutionary structures. Finally, we use the SEv-LSP model to demonstrate the evolving dynamics between the hippocampus and the nucleus accumbens during an associative learning experiment. Supplementary materials for this article are available online.
Bibliographical noteFunding Information:
We thank the associate editor and three anonymous referees for their comments that have led to an improved article. Research of H. Ombao is supported in part by grants from NSF DMS: 1509023 and NSF MMS: 1461534. H. Ombao also gratefully acknowledges discussions with the UC Irvine Space-Time Modeling group.
© 2016 American Statistical Association.
- Bivariate time series
- Local stationarity
- Replicated time series
- Signal heterogeneity
- Spectral analysis