In the last past years the liberalization of the electricity supply, the increase variability of electric appliances and their use, and the need to respond to the electricity demand in the real time had made electricity demand forecasting a challenge. To this challenge, many solutions are being proposed. The electricity demand involves many sources such as economic activities, household need and weather sources. All this sources make hard electricity demand forecasting. To forecast the electricity demand, some proposed parametric methods that integrate main variables that are sources of electricity demand. Others proposed non parametric method such as pattern recognition methods. In this paper we propose to take only the past electricity consumption information embedded in a functional vector autoregressive state space model to forecast the future electricity demand. To estimate the parameters of this model we use likelihood maximization, spline smoothing, functional principal components analysis and Kalman filtering. The principal advantage of this model is to forecast electricity demand without taking into account exogenous variables in case of stationary We have seen that in that case the results of the model are competitive and not competitive for non stationary case. But in case of non stationary, this model allows to integrate exogenous variables.