S3RI Seminar - Quantile Spectral Analysis for Locally Stationary Time Series, Marc Hallin, ECARES Seminar

Event details

Classical spectral methods are subject to two fundamental limitations: they only can account for covariance-rela​ted serial dependencies, and they require second-order stationarity. Much attention has been devoted lately to quantile (copula-based) spectral methods that go beyond traditional covariance-base​d serial dependence features. At the same time, covariance-base​d methods relaxing stationarity into much weaker local stationarity conditions have been developed for a variety of time-series models. Here, we are combining those two approaches by proposing copula-based spectral methods for locally stationary processes. We therefore introduce a time-varying version of the copula spectra that have been recently proposed in the literature, along with a suitable local lag-window estimator. We propose a new definition of local strict stationarity that allows us to handle completely general non-linear processes without any moment assumptions, thus accommodating our copula-based concepts and methods. We establish a central limit theorem for the new estimators, and illustrate the power of the proposed methodology by means of a simulation study. Moreover, real-data applications demonstrate that the new approach detects important variations in serial dependence structures both across time and across quantiles. Such variations remain completely undetected, and are actually undetectable, via classical covariance-base​d spectral methods. Based on joint work with Stefan Birr (Ruhr-Universit​ät Bochum), Holger Dette (Ruhr-Universit​ät Bochum), Tobias Kley (London School of Economics) and Stanislav Volgushev (University of Toronto). The main reference (JRSSB 2017 DOI: 10.1111/rssb.12​231) is available online: http://onlineli​brary.wiley.com​/doi/10.1111/rs​sb.12231/full The seminar will also be available via a live web-cast at https://coursec​ast.soton.ac.uk​/Panopto/Pages/​Viewer.aspx?id=​4cb95fc7-eda0-4​ec4-ab1c-706495​cb906b