Regressions with Heavy Tailed Weakly Nonstationary Processes

Friday May 3, 2pm, Carslaw 373

Ioannis Kasparis (University of Cyprus, Department of Economics)

Title: Regressions with Heavy Tailed Weakly Nonstationary Processes

We develop a limit theory for general additive functionals of Weakly Nonstationary Processes (WNPs) under heavy tailed innovations. In particular, we assume WNPs driven by innovations that are in the domain of attraction of an α-stable law with stability parameter α∈(0,2]. The current work generalises the recent limit theory of Duffy and Kasparis (2018), who consider WNPs under second moments. The defining characteristic of WNPs is that their empirical versions, upon standardisation, converge weakly to white noise processes rather than fractional Gaussian or fractional stable motions, which is typically the case under nonstationarity. As a consequence, the usual asymptotic methods (i.e. FCLTs) are not applicable, and different methods are required. The leading examples of WNPs under consideration are fractional d=1-1/α and mildly integrated processes driven by heavy tailed errors. Our main limit results are utilised for the asymptotic analysis both parametric and nonparametric regression estimators.
Joint work with S. Arvanitis (Athens University of Economics & Business) and J.A. Duffy (Oxford).