Wavelet-based estimation for Gaussian time series and spatio-temporal processes
Wenjun Zheng · OhioLink ETD Center (Ohio Library and Information Network) · 2014
Modern statistical analyses often require the modeling non-Markov time series and spatio-temporal dependencies.Traditional likelihood methods are computationally demanding for these models, leading us to consider approximate likelihood methods that are computationally efficient, while not overly compromising on the efficiency of the parameter estimates.In this dissertation various wavelet-based Whittle approximations are investigated to model a certain class of nonstationary Gaussian time series and a class of Gaussian spatio-temporal processes.Wavelet transforms can help decorrelate processes across and within wavelet scales, allowing for the simplified modeling of time series and spatio-temporal processes.In addition to being computationally efficient, the proposed maximum wavelet-Whittle likelihood estimators of a Gaussian process are shown to be asymptotically normal.Asymptotic properties of the estimators are verified in simulation studies, demonstrating that the typical independence everywhere assumption assumed for wavelet-based estimation is not optimal.These methods are applied to the analyses of a Southern Oscillation Index climate series and the Irish wind speed data.