Equation-by-equation estimation of multivariate periodic electricity price volatility

Electricity prices are characterised by strong autoregressive persistence, periodicity (e.g. intraday, day-of-the week and month-of-the-year effects), large spikes or jumps, GARCH and - as evidenced by recent findings - periodic volatility. We propose a multivariate model of volatility that decomposes volatility multiplicatively into a non-stationary (e.g. periodic) part and a stationary part with log-GARCH dynamics. Since the model belongs to the log-GARCH class, the model is robust to spikes or jumps, allows for a rich variety of volatility dynamics without restrictive positivity constraints, can be estimated equation-by-equation by means of standard methods even in the presence of feedback, and allows for Dynamic Conditional Correlations (DCCs) that can - optionally - be estimated subsequent to the volatilities. We use the model to study the hourly day-ahead system prices at Nord Pool, and find extensive evidence of periodic volatility and volatility feedback. We also find that volatility is characterised by (positive) leverage in one third of the hours, and that a DCC model provides a better fit of the conditional correlations than a Constant Conditional Correlation (CCC) model.