\section{Electricity Price Data}\index{electricity price data}

In this chapter, the daily spot price at the Nordic Power Exchange, Nord Pool, is studied. It will be the price at 9 a.m. for a ten year period, from 01.01.2000 to 31.12.2009. The price region considered is the middle of Norway. It should be noted that this price region was established on 20.11.2006. Before that time, it was integrated with the rest of Norway. It is also worth mentioning that the spot price in this market is actually a 1-day futures price, where the price for the following day is set by an auction at noon. 

Plotted in Figure~\ref{fig:dailyp} are the daily prices observed over this ten year period, and in Figure~\ref{fig:dailypx} are the daily price changes, presented as logarithmic returns. Observable from these figures are large spikes in both the price and price change processes. There also seems to be some volatility clustering in the return series. In Table~\ref{tab:desstat}, some descriptive statistics is presented along with test values for the Ljung--Box test \citep{BROCKWELL} for different lags on both the return and squared return series. $Q(h)$ denotes the test statistic at lag $h$ for the return series, while $Q^2(h)$ is the same for the squared series. A large excess kurtosis and positive skewness are observed, meaning that both very small and very large price changes occur often compared to a normal distribution, and large positive price changes are more common than the large negative price changes. From the Ljung--Box test, significant serial correlation for all lags considered here is observed, which is expected. For the squared returns, there is significant serial correlation for both 7 and 10 lags, meaning that there is significant volatility clustering or a GARCH effect.

\begin{table}
	\begin{center}
	\caption{Descriptive statistics for the return series.}\label{tab:desstat}
	\begin{tabular}{c c c c c c c c c}
	Mean & Skew. & Ex.Kurt. & $Q(1)$ & $Q(2)$ & $Q(7)$ & $Q^2(1)$ & $Q^2(2)$ & $Q^2(7)$ \\
	\hline
	$3.00\cdot10^{-4}$ & $0.97$ & $23.27$ & $182.20$ & $430.86$ & $1505.67$ & $265.50$ & $606.49$ & $863.32$ 
	\end{tabular}
	\end{center}
\end{table}
%% From these plots, and from \cite{SOLIBAKKE_2002} and \cite{FongChan2006283}, we observe that the data are highly seasonal and displays significant volatility clustering and serial correlation. It should also be noted that we are going to model the left and right tails of the distribution independent of eachother.

\begin{figure}
	\begin{center}
		\includegraphics[width=0.8\textwidth]{Figures/dailyprices.pdf}
		\caption{Daily electricity spot prices on Nord Pool for the ten year period.}
		\label{fig:dailyp}
	\end{center}
\end{figure}

\begin{figure}
	\begin{center}
		\includegraphics[width=0.8\textwidth]{Figures/dailypriceschanges.pdf}
		\caption{Daily electricity price changes on Nord Pool for the ten year period.}
		\label{fig:dailypx}
	\end{center}
\end{figure}

