machine learning models for the quarterly predictions would not have added any extra value over the benchmark. Lastly, the strategies based on the monthly predictions were all better than a strategy where all contracts were purchased. Out of the presented models, ridge regression, which was the second best on the training set, had the best performance in predicting monthly prices of 2018. The runner-up was SVR, which performed best on the training set.
As discussed in Section 2.4, the actual prices in 2018 were quite extreme and far from what was anticipated at the start of the year. Moreover, the prices were extreme compared to the other prices of our data set, which begins in 2013. The average system price for 2018 was higher than all years included, and the last two quarters of 2018 were substantially higher than all other quarters. Likewise, the average monthly system prices in July, August, September, November and December were higher than all other observed months, and June and October were higher than the corresponding months all previous years.
Thus, the prediction accuracy of our models must be viewed in light of other predictions.
5.3 Comparison with other predictions
The particular situation of 2018 has to be taken into account considering that our price predictions were generally lower than the actual prices. Both contract prices and our model predictions hit relatively poorly. Especially the yearly price predictions and the monthly and quarterly predictions for the summer months were far off. The contract prices were far from the system price some of these months. However, these were still far closer to the actual system price than the model predictions. In the following, we will look at whether other sources performed better in predicting the prices for 2018. First we will briefly mention what other analysts expected that system prices would be in 2018.
Thereafter, bringing back the second hypothesis mentioned in Section 4.1.1 of how to best predict Nordic system prices, we will introduce the forecasts made by the ARIMA and NNAR model. The expectations and forecasts will be used to evaluate the performance of the machine learning predictions.
64 5.3 Comparison with other predictions
5.3.1 Market expectations of 2018
On December 1st, 2017, the price of the yearly contract for 2018 was of 26.90 euros per MWh, reflecting the market’s expectations. In hindsight, this price turned out to be far too low. On January 23rd, the energy trading group Energi Salg Norge (2018a) stated that due to the strong hydrological situation in the Nordic countries, there was no pressure on the supply situation in the forthcoming months. However, on March 26th, the same source noted that the Nordic hydro balance had turned to a deficit, pointing towards high spot prices during the spring (Energi Salg Norge, 2018b). Power distributor Kraftriket stated on April 6th that even though the expected price development for spring and summer were somewhat higher prices than the previous year, the expectation was still declining prices (Kraftriket, 2018). However, because of the warm and dry summer, prices became record high and July 2018 had the highest registered July price of all times (Hovland, 2018a). Power analyst John Brottemsmo of Kinect Energy group predicted that if the fall turned dry, Nordic prices could end up at 60-70 euros per MWh. By September, storms and heavy rainfall followed the dry summer (Hovland, 2018b). As such, hydro reservoirs started filling up. Brottemsmo then stated that with current outlooks, prices were expected to continue falling, though there was much uncertainty as reservoir levels were still low. To summarize, the uncertainty related to the development of prices in 2018 was high, and several predictions proved wrong.
5.3.2 Forecasts made by ARIMA and NNAR
In the following, we compare the results of the ARIMA and NNAR models with the predictions introduced in Section 5.1. A complete overview of the predicted prices for each period are included in Table A3.1 and A3.2 in Appendix A3. Estimating the models on data up until December 2017, ARIMA(1,1,0)(2,0,0)12 and NNAR(1,1,2)12 models were chosen. The ARIMA model thus generated the forecast using one lagged value of the price and two seasonally lagged values. In addition, the series was differenced once to assure stationarity. The NNAR model made use of one lagged value of the system price, one seasonally lagged value and two hidden nodes to predict future values of the system price.
5.3 Comparison with other predictions 65
Figure 5.7: Yearly system price, contract price, predicted price and forecasted prices
In the yearly prediction of 2018 ARIMA forecasted an average power price of 33.32 euros per MWh, and NNAR 35.17 euros per MWh. These prices are illustrated along with the actual system price, the contract price and the prediction made by random forests in Figure 5.7 As can be seen in the plot, NNAR was the forecast closest to the system price.
Nevertheless, forecasts by both ARIMA and NNAR were quite far from the system price of 43.99 euros, however, they were still closer to the actual system price than all machine learning predictions and the contract price were. Using the forecasts on the decision date would thus have rendered the optimal strategy of not purchasing the futures contract.
Figure 5.8: Quarterly system prices, contract prices, predicted prices and forecasted prices
66 5.3 Comparison with other predictions
In Figure 5.8 the quarterly forecasts based on ARIMA and NNAR are illustrated against the system price, contract price and the predicted price from ridge regression. Out of the two forecasts, NNAR was once again closest to the system price, and like the yearly term, both forecasts were closer to the actual prices than the ridge regression prediction. The NNAR forecast was also more accurate than the contract price in all quarters but the third. It would also have led to a better strategy than ridge regression did, by purchasing futures contracts only for the third and fourth quarter. Still, both the ARIMA and NNAR forecasts were quite far from the system price. Moreover, these forecasts followed the same pattern as the predictions, as the price decreased towards the third quarter instead of increasing as the system price did. The forecasted prices increased again towards the last quarter.
Figure 5.9: Monthly system prices, contract prices, predicted prices and forecasted prices
In Figure 5.9, the monthly forecasts from ARIMA and NNAR are plotted against the monthly system prices and SVR predictions. The same lagged effect that was seen for the predictions also occurred for the forecasts, as if information is conceived too late. In general, the ARIMA and NNAR forecasts followed each other quite closely and were on a higher price level than the SVR predictions. Although both forecast models predicted too low prices in the summer months, the predicted prices were not as low as those made by the machine learning models. Altogether, NNAR was closest to the actual system prices, however contract prices were on average marginally closer. A hedging strategy based on