Caitlin Berry, Department of Applied Mathematics, University of Colorado Boulder

Subordinated Processes and Spectral Analysis for Time Series

The overarching theme for this talk is models for nonstationary, non-Gaussian, high frequency time series data with various applications. The first prong of my research is concerned with using time-changed Gaussian processes to simulate high frequency solar irradiance data. The second piece extends this idea of singularly time-changed processes to deeply subordinated jump diffusion processes with application to cryptocurrency returns. The third section of the talk will propose a project which delves into the spectral world of time series analysis applied to fractional frequency deviates of atomic clocks in the hopes of improving current methods of inter-day uncertainty estimates for these data.