## Modellering og forecast af spotpriserne på el vha. SARFIMA-modeller med regimeskift

Studenteropgave: Speciale (inkl. HD afgangsprojekt)

• Simon Møller
• Julie Brandt
4. semester, Matematik-Økonomi (cand.scient.oecon.), Kandidat (Kandidatuddannelse)
This thesis is concerned with the modelling and forecasting of electricity spot prices in select areas of the Nordpool Spot market. The day-ahead market prices are extracted from five different bidding areas, and these price series form the basis for further investigations.

The spot price data exhibit huge fluctuations and outliers, which are typical for energy prices. However, the prices still tend to revert to a certain mean level. Each bidding area is connected to one or several bidding areas, thus enabling the transmission of electricity between areas. When there is no congestion in an interconnection, prices in the connected areas will be identical, and congestion, on the other hand, will lead to different prices. There are five different connections between the five selected bidding areas, and in approximately 40-90% of the time, prices are identical across two neighboring areas. The data clearly exhibit a seasonal pattern; prices are usually higher on weekdays than in weekends. Furthermore, prices also show a clear seasonal pattern in terms of time of day and month of the year.

The plotting of the sample auto covariance functions of the price series clearly shows the presence of long memory in the data. This motivates the use of a seasonal fractional ARIMA (SARFIMA) model for modelling and forecasting. Initially, the data will be adjusted for seasonality by means of linear regression on linear trend and dummy variables representing time of day, day of week, and month of year. The resulting seasonally adjusted prices are then to be modelled and forecasted using a SARFIMA model.

The influence of congestion in connections between bidding areas prompts a further modification of the SARFIMA model; the states of congestion and non-congestion, respectively, define the two regimes of a regime-switching SARFIMA model, thus allowing a different set of parameters to be estimated for each regime. A Markov chain determines the switching between regimes.

For each connection, a non-regime-switching and a regime-switching SARFIMA model are estimated for the time series of the spot price in each of the two connected areas and the price difference. Because the regimes are observable, the model parameters can be estimated by conditional maximum likelihood.

The implementation of the model parameter estimation has been carried out using the R programming language. The estimation process involves nonlinear numerical optimization powered by the L-BFGS algorithm. Model estimation has proven to be considerably time consuming, especially regarding the estimation of parameters for the regime-switching models.

The model forecasts have been produced using Monte Carlo simulations.

Finally, forecast results from both the non-regime-switching and the regime-switching SARFIMA model are plotted and examined. In general, the non-regime-switching SARFIMA model quite surprisingly manages to outperform the regime-switching model in terms of forecast accuracy.
Sprog Dansk 11 jun. 2014 124 Department of Mathematical Sciences, Aalborg University
ID: 198702290