Novel periodic extensions of dynamic long-memory regression models with autoregressive conditional heteroscedastic errors are considered for the analysis of daily electricity spot prices. The parameters of the model with mean and variance specifications are estimated simultaneously by the method of approximate maximum likelihood. The methods are implemented for time series of 1,200-4,400 daily price observations in four European power markets. Apart from persistence, heteroscedasticity, and extreme observations in prices, a novel empirical finding is the importance of day-of-the-week periodicity in the autocovariance function of electricity spot prices. In particular, the very persistent daily log prices from the Nord Pool power exchange of Norway are effectively modeled by our framework, which is also extended with explanatory variables to capture supply-and-demand effects. The daily log prices of the other three electricity markets - EEX in Germany, Powernext in France, and APX in The Netherlands - are less persistent, but periodicity is also highly significant. The dynamic behavior differs from market to market and depends primarily on the method of power generation: hydro power, power generated from fossil fuels, or nuclear power. The article improves on existing models in capturing the memory characteristics, which are important in derivative pricing and real option analysis. © 2007 American Statistical Association.