Statistics and Its Interface

Volume 16 (2023)

Number 1

Special issue on recent developments in complex time series analysis – Part I

Guest editors: Robert T. Krafty (Emory Univ.), Guodong Li (Univ. of Hong Kong), Anatoly Zhigljavsky (Cardiff Univ.)

Generalized Gaussian time series model for increments of EEG data

Pages: 17 – 29



Nikolai N. Leonenko (School of Mathematics, Cardiff University, Cardiff, Wales, United Kingdom)

Zeljka Salinger (School of Mathematics, Cardiff University, Cardiff, Wales, United Kingdom)

Alla Sikorskii (Departments of Psychiatry and Statistics and Probability, Michigan State University, East Lansing, Mich., U.S.A.)

Nenad Suvak (Department of Mathematics, J.J. Strossmayer University of Osijek, Croatia)

Michael Boivin (Departments of Psychiatry and Neurology and Ophtalmology, Michigan State University, East Lansing, Mich., U.S.A.)


We propose a new strictly stationary time series model with marginal generalized Gaussian distribution and exponentially decaying autocorrelation function for modeling of increments of electroencephalogram (EEG) data collected from Ugandan children during coma from cerebral malaria. The model inherits its appealing properties from the strictly stationary strong mixing Markovian diffusion with invariant generalized Gaussian distribution (GGD). The GGD parametrization used in this paper comprises some famous light-tailed distributions (e.g., Laplace and Gaussian) and some well known and widely applied heavy-tailed distributions (e.g., Student). Two versions of this model fit to the data from each EEG channel. In the first model, marginal distributions is from the light-tailed GGD sub-family, and the distribution parameters were estimated using quasi-likelihood approach. In the second model, marginal distributions is heavy-tailed (Student), and the tail index was estimated using the approach based on the empirical scaling function. The estimated parameters from models across EEG channels were explored as potential predictors of neurocognitive outcomes of these children 6 months after recovering from illness. Several of these parameters were shown to be important predictors even after controlling for neurocognitive scores immediately following cerebral malaria illness and traditional blood and cerebrospinal fluid biomarkers collected during hospitalization.


time series, diffusion process, diffusion discretization, generalized Gaussian distribution, heavy-tailed distribution, tail index

2010 Mathematics Subject Classification

Primary 37M10. Secondary 62G07, 62J20, 62M10, 62P10.

Z. Salinger was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership (project reference 2275322).

Received 19 April 2021

Accepted 11 July 2021

Published 28 December 2022