Bayesian Inference for a Periodic Stochastic Volatility Model of Intraday Electricity Prices

Michael S. Smith, Melbourne Business School

Abstract

The Gaussian stochastic volatility model is extended to allow for periodic autoregressions (PAR) in both the level and log-volatility process. Each PAR is represented as a first order vector autoregression for a longitudinal vector of length equal to the period. The periodic stochastic volatility model is therefore expressed as a multivariate stochastic volatility model. Bayesian posterior inference is computed using a Markov chain Monte Carlo scheme for the multivariate representation. A circular prior that exploits the periodicity is suggested for the log-variance of the log-volatilities. The approach is applied to estimate a periodic stochastic volatility model for half-hourly electricity prices with period m = 48. Demand and day types are included in both the mean and log-volatility equations as exogenous effects. A nonlinear relationship between demand and mean prices is uncovered which is consistent with economic theory, and the predictive density of prices evaluated over a horizon of one week. Overall, the approach is shown to have strong potential for the modelling of periodic heteroscedastic data.