Electric Consumption Curves Analysis by Hidden Markov Chains
We develop an approach based on hidden Markov chains for the modelling and statistical analysis of electric consumption curves. A preliminary analysis of variance leads to the estimation of effects on fixed factors (month, day, hour, type of contract and maximal power) on the log-consumption. Then the residuals are modelled with a hidden Markov chain. The hidden states are restored and interpreted using a contingency table relating the restored hidden states with the consumption of various electrical devices when available. We show how the consumption induced by each device can be estimated, from the restored states and the contingency table. The estimates are made more realistic by taking advantage of prior information on the consumption. Finally, we deal with model selection issues. The usual criteria select too complex models, and thus do not help relating hidden state with the device consumption in a clear way. We present alternative selection methods taking into account of the pupose of linking hidden states and consumption groups.