Multivariate modelling of weather variables

Renewable energy production and electricity consumption both depend heavily on weather: temperature, precipitations, wind, solar radiation... Thus, making impact studies on the supply/demand equilibrium may require a weather generator, that is a model capable of quickly simulating long, realistic time series of weather variables, at the daily time step. To this aim, one of the possible approaches is using hidden Markov models: we assume that the evolution of the weather variables are governed by a latent variable that can be interpreted as a weather type. Using this approach, we propose a model able to simulate simultaneously temperature, wind speed and precipitations, accounting for the specific non-stationarities of weather variables. Besides, we study some theoretical properties of cyclo-stationary hidden Markov models: we provide simple conditions of identifiability and we show the strong consistency of the maximum likelihood estimator. We also show this property of the MLE for hidden Markov models including long-term polynomial trends. (author)