  The spectral distribution $f(\omega)$ of a stationary time series
$\{Y_t\}_{t\in\mathbb{Z}}$ can be used to investigate whether or not periodic
structures are present in $\{Y_t\}_{t\in\mathbb{Z}}$, but $f(\omega)$ has some
limitations due to its dependence on the autocovariances $\gamma(h)$. For
example, $f(\omega)$ can not distinguish white i.i.d. noise from GARCH-type
models (whose terms are dependent, but uncorrelated), which implies that
$f(\omega)$ can be an inadequate tool when $\{Y_t\}_{t\in\mathbb{Z}}$ contains
asymmetries and nonlinear dependencies.
  Asymmetries between the upper and lower tails of a time series can be
investigated by means of the local Gaussian autocorrelations introduced in
Tj{\o}stheim and Hufthammer (2013), and these local measures of dependence can
be used to construct the local Gaussian spectral density presented in this
paper. A key feature of the new local spectral density is that it coincides
with $f(\omega)$ for Gaussian time series, which implies that it can be used to
detect non-Gaussian traits in the time series under investigation. In
particular, if $f(\omega)$ is flat, then peaks and troughs of the new local
spectral density can indicate nonlinear traits, which potentially might
discover local periodic phenomena that remain undetected in an ordinary
spectral analysis.
