|
Abstract:
|
Modern approaches to modeling sequence data with long-range dependencies have largely sought to capture this property through time-domain representations. By contrast, theoretical formulations of long-range dependence in the stochastic process literature find their clearest expression in the frequency domain. We contribute a modeling approach for long-range dependent data from this frequency-domain perspective, which allows for the development of expressive spectral representations. We propose and implement a fast alternating proximal gradient method to estimate both the long memory parameter and a flexible component-wise representation of the short-range dependent spectrum in an appropriate function space. We illustrate the method in an application to multivariate local field potential (LFP) recordings in the rhesus macaque cortex, in which analysis of both long memory and the estimated cross-spectrum is of scientific interest.
|
