This paper deals with the modeling of complex stochastic processes in the long-term multistage energy planning problem which is characterized by the presence of many sources of uncertainty, both in the objective function and in the constraints. Starting from basic projec- tions consisting of ranges for the future values of parameters such as demands, energy costs and technology efficiencies, we model the temporal correlation of these uncertain parameters through auto-regressive models. Due to the distinct role played by these parameters in the model, some of them require discretization via Markov chains. The resulting formulation is then solved with an advanced SDDP algorithm available in the literature that handles finite-state Markov chains. Our numerical experiments, performed on the Swiss energy system, show a very desirable adaptation strategy of investment decisions to uncertainty scenarios, a behavior that is not observed when the temporal correlation is ignored. Moreover, the solutions lead to better out-of-sample cost performances than the non-correlated ones which usually yield overcapacities to protect against high, but unlikely, parameter variations over time.