Scenario generation and probabilistic forecasting analysis of spatio-temporal wind speed series with multivariate autoregressive volatility models

This paper evaluates the application of a family of VAR-mGARCH (Vector AutoRegressive with multivariate AutoRegressive Conditional Heteroskedasticity) volatility models to the problem of modeling (i.e. generating correct in-sample scenarios) and forecasting in a probabilistic way three univariate but mutually dependent wind speed hourly series. The evaluation starts from the consideration that optimal modeling and optimal forecasting are not necessarily attained by the same models, and that they are assessed in different ways. The proposed VAR-mGARCH family, originated in Finance, consists of the VAR-BEKK (VAR - Baba, Engle, Kraft and Kroner) model and the VAR-DCC (VAR - Dynamic Conditional Correlation) model, the latter seen as the simplified and more scalable version of the former. These models were never used in wind speed studies before. Both models will be used with Gaussian innovations, and the VAR-DCC model will be also used with Student’s t innovations. These models, which are able to dynamically couple volatilities, are compared to two benchmark model sets, the first set consisting of three independent univariate AR-GARCH (i.e. non-vector) models, the second set consisting of an individual VAR model without the GARCH sector. These benchmark models cannot dynamically couple volatilities. Both benchmark model sets will be used with Gaussian innovations. The time series used for the evaluation are taken from three North-American wind metering sites located at few tens of kilometers from each other. In order to highlight the usefulness of choosing autoregressive coupled volatility schemes for modeling and forecasting spatially and temporally varying wind speed data, a controlled variance electricity generation portfolio example of Markowitz type, typical of Energy Finance, is also discussed at some length. In all, it is concluded that the VAR-DCC model with Student’s t innovations is the most balanced choice for this data set when the three goals of modeling, forecasting and scalability in the number of considered sites are taken into account at once.