Abstract

This talk will consider wavelet-based methods for long memory estimation. Data from long memory processes have the distinctive feature that the correlation between distant observations is not negligible. Wavelets, being self-similar, have a strong connection to long memory processes and have proven to be a powerful tool for the analysis and synthesis of data from such processes. Here, in particular, we will employ discrete wavelet transforms to simplify the dense variance-covariance matrix of the error structure. We first describe a wavelet-based Bayesian procedure for the estimation and location of multiple change points in the long memory parameter of Gaussian ARFIMA models. We then turn our attention to linear regression models with long memory errors and stage a Bayesian approach to inference in the wavelet domain. Linear regression models with long memory errors have proven useful for applications in many areas, such as medical imaging, signal processing, and econometrics. Recent successful applications include fMRI image data. In this talk we will consider experimental data from human cognitive tasks.