  In this paper, dual generalized long memory modelling has been proposed to
predict the electricity spot price. First, we focus on modelling the
conditional mean of the series so we adopt a generalized fractional k-factor
Gegenbauer process ( k-factor GARMA). Secondly, the residual from the k-factor
GARMA model has been used as a proxy for the conditional variance; these
residuals were predicted using two different approaches. In the first approach,
a local linear wavelet neural network model (LLWNN) has developed to predict
the conditional variance using two different learning algorithms, so we
estimate the hybrid k- factor GARMA-LLWNN based backpropagation (BP) algorithm
and based particle swarm optimization (PSO) algorithm. In the second approach,
the Gegenbauer generalized autoregressive conditional heteroscedasticity
process (G-GARCH) has been adopted, and the parameters of the k-factor GARMAG-
GARCH model have been estimated using the wavelet methodology based on the
discrete wavelet packet transform (DWPT) approach. To illustrate the usefulness
of our methodology, we carry out an empirical application using the hourly
returns of electricity prices from the Nord Pool market. The empirical results
have shown that the k-factor GARMA-G-GARCH model has the best prediction
accuracy in terms of forecasting criteria, and find that this is more
appropriate for forecasts.
