| Abstract: |
We discuss stochastic modeling of volatility persistence and anti-correlations
in electricity spot prices, and for this purpose we present two mean-reverting
versions of the multifractal random walk (MRW). In the first model the
anti-correlations are modeled in the same way as in an Ornstein-Uhlenbeck
process, i.e. via a drift (damping) term, and in the second model the
anti-correlations are included by letting the innovations in the MRW model be
fractional Gaussian noise with H < 1/2. For both models we present approximate
maximum likelihood methods, and we apply these methods to estimate the
parameters for the spot prices in the Nordic electricity market. The maximum
likelihood estimates show that electricity spot prices are characterized by
scaling exponents that are significantly different from the corresponding
exponents in stock markets, confirming the exceptional nature of the
electricity market. In order to compare the damped MRW model with the
fractional MRW model we use ensemble simulations and wavelet-based variograms,
and we observe that certain features of the spot prices are better described
by the damped MRW model. The characteristic correlation time is estimated to
approximately half a year. |