Title: Nonlinear spectral analysis: A local Gaussian approach
Speaker: Lars Arne Jordanger, IDER, HVL
The spectral distribution f(ω) can detect periodicites in a stationary time series Yt, but it has some limitations due to its dependence on the autocorrelations ρ(h). f(ω) completely determines Gaussian time series, but it is an inadequate tool when Yt contains asymmetries and nonlinear dependencies (it can e.g. not distinguish white i.i.d. noise from GARCH-type models, whose terms are dependent, but uncorrelated). A local Gaussian spectral distribution fv(ω) enables a local investigation of Yt by replacing the autocorrelations ρ(h) with local Gaussian autocorrelations ρv(h). A key feature of fv(ω) is that it coincides with f(ω) for Gaussian time series, which implies that fv(ω) can be used to detect non-Gaussian traits in other time series. If f(ω) is flat, then peaks and troughs of fv(ω) can indicate nonlinear traits, which potentially might discover local periodic phenomena that goes undetected in an ordinary spectral analysis.