Speaker: Rasmus Søndergaard Pedersen, University of Copenhagen (https://www.econ.ku.dk/ansatte/vip/?pure=da/persons/303839)

Title: On testing for zero mean of a (potentially) heavy-tailed time series

Abstract:
We propose a unified, model-free approach for testing whether a stationary time series has zero mean, robust to heavy-tailed distributions, including those with infinite variance. The method employs a test statistic given as a ratio of sample moments and is based on a novel stable limit theorem for strongly mixing processes. The limiting distribution of the test statistic depends on the tail behavior of the series, and we evaluate the adequacy of standard subsampling techniques for critical value construction. These techniques are known to be valid under both the null hypothesis of zero mean and alternatives with a finite non-zero mean, regardless of the degree of tail heaviness. However, we show that they offer no (non-trivial) power against alternatives where the mean does not exist. To address this limitation, we introduce a modified test statistic along with an adapted subsampling procedure. As an empirical application, we revisit the Diebold-Mariano test for equal predictive ability of forecast series.

Host: Mikkel Bennedsen

Organisers: Stefán Guðmundsson and Mikkel Sølvsten