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We discuss stochastic modeling of volatility persistence andanti-correlations in electricity spot prices, and for this purpose we presenttwo mean-reverting versions of the multifractal random walk (MRW). In the firstmodel the anti-correlations are modeled in the same way as in anOrnstein-Uhlenbeck process, i.e. via a drift (damping) term, and in the secondmodel the anti-correlations are included by letting the innovations in the MRWmodel be fractional Gaussian noise with H < 1/2. For both models we presentapproximate maximum likelihood methods, and we apply these methods to estimatethe parameters for the spot prices in the Nordic electricity market. Themaximum likelihood estimates show that electricity spot prices arecharacterized by scaling exponents that are significantly different from thecorresponding exponents in stock markets, confirming the exceptional nature ofthe electricity market. In order to compare the damped MRW model with thefractional MRW model we use ensemble simulations and wavelet-based variograms,and we observe that certain features of the spot prices are better described bythe damped MRW model. The characteristic correlation time is estimated toapproximately half a year.

Modeling electricity spot prices using mean-reverting multifractal processes