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Title: Nonlinear spectral analysis: A local Gaussian approach Authors:  Lars Arne Jordanger - Western Norway University of Applied Sciences (Norway) [presenting]
Dag Tjoestheim - University of Bergen (Norway)
Abstract: The spectral distribution $f(\omega)$ can detect periodicites in a stationary time series $Y_{t}$, but it has some limitations due to its dependence on the autocorrelations $\rho(h)$. $f(\omega)$ completely determines Gaussian time series, but it is an inadequate tool when $Y_t$ 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 $f_v(\omega)$ enables a local investigation of $Y_t$ by replacing the autocorrelations $\rho(h)$ with local Gaussian autocorrelations $\rho_v(h)$. A key feature of $f_v(\omega)$ is that it coincides with $f(\omega)$ for Gaussian time series, which implies that $f_v(\omega)$ can be used to detect non-Gaussian traits in other time series. If $f(\omega)$ is flat, then peaks and troughs of $f_v(\omega)$ can indicate nonlinear traits, which potentially might discover local periodic phenomena that goes undetected in an ordinary spectral analysis.