  Here we develop the theory of seasonal FIEGARCH processes, denoted by
SFIEGARCH, establishing conditions for the existence, the invertibility, the
stationarity and the ergodicity of these processes. We analyze their asymptotic
dependence structure by means of the autocovariance and autocorrelation
functions. We also present some properties regarding their spectral
representation. All properties are illustrated through graphical examples and
an application of SFIEGARCH models to describe the volatility of the S&P500 US
stock index log-return time series in the period from December 13, 2004 to
October 10, 2009 is provided.
