We analyze Australian electricity price returns and find that they exhibit volatility clustering, long memory, structural breaks, and multifractality. Consequently, we let the return mean equation follow two alternative specifications, namely (i) a smooth transition autoregressive fractionally integrated moving average (STARFIMA) process, and (ii) a Markov-switching autoregressive fractionally integrated moving average (MSARFIMA) process. We specify volatility dynamics via a set of (i) short- and long-memory GARCH-type processes, (ii) Markov-switching (MS) GARCH-type processes, and (iii) a Markov-switching multifractal (MSM) process. Based on equal and superior predictive ability tests (using MSE and MAE loss functions), we compare the out-of-sample relative forecasting performance of the models. We find that the (multifractal) MSM volatility model keeps up with the conventional GARCH- and MSGARCH-type specifications. In particular, the MSM model outperforms the alternative specifications, when using the daily squared return as a proxy for latent volatility.
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