A Hawkes Model Approach to Modeling Price Spikes in the Japanese Electricity Market

Abstract

The Japan Electric Power Exchange (JEPX) provides a platform for the trading of electric energy in a manner similar to more traditional financial markets. As the number of market agents increase, there is an increasing need for effective price-forecasting models. Electricity price data are observed to exhibit periods of relatively stable, i.e., low-magnitude, low-variance prices interspersed with periods of higher prices accompanied by larger uncertainty. The price data time series therefore exhibits a temporal non-stationarity characteristic that is difficult to capture with typical time series modeling frameworks. In this paper, we implement models for the occurrence of price spike events where spikes are defined as observing prices above a predefined threshold set here at 25 JPY/kWh. This value corresponds to about the 90th percentile of observed prices during peak trading periods. The price spikes time series is observed to be rare events that occur in clusters. We therefore propose to model the data as a Hawkes process whereby the occurrence of a spike event increases the probability of observing more spikes in the period immediately following a price spike event. We test two variations of the classical Hawkes model: the first variation models the change in the magnitude of the underlying intensity as a function of the magnitude of the price spike while the second variation models the change in the decay rate of the underlying intensity as a function of the magnitude of the price spike. An analysis of the performance of the models based on the mean absolute error (MAE) of the spike occurrence probability, a weighted accuracy index, and the Matthews correlation coefficient (MCC) metrics shows the effectiveness of the variable magnitude variation of the Hawkes model in generating short-term forecasts of the occurrence of price spike events. The modified Hawkes model especially outperforms other candidate models as the length of the forecasting horizon increases.