Multivariate long-memory modeling: applications to EDF's producer issues in the context of the liberalization of the European electricity market.

Summary Several financial market data, such as spot prices of interconnected European electricity markets, exhibit long memory, in the sense of hyperbolic decay of autocorrelations combined with heteroskedasticity and periodic or non periodic cycles. To model such behaviors, we introduce k-factor GIGARCH processes and propose two parameter estimation methods. We develop the asymptotic properties of the estimators of each method. Moreover, in order to compare the asymptotic properties of the estimators, Monte Carlo simulations are performed. On the other hand, we propose a multivariate generalized long-memory model (k-factor MVGARMA) to jointly model two interconnected European electricity markets. We give a practical procedure for parameter estimation. For forecasting, we provide analytical expressions for the least squares predictors for the proposed models and confidence intervals for the forecast errors. Finally, we apply these two models on the spot electricity prices of the French and German markets and compare their predictive capabilities.