Load flow analysis is an essential part of system operation and planning. Up to now, load flow can be categorized as deterministic and probabilistic. In the deterministic load flow, the generations and loads are fixed. However, the state variables of power systems have uncertain nature due to the random load variations and stochastic distributed generations. In this regard, the probabilistic load flow (PLF) is implemented. The inputs of PLF are probability density functions (PDFs) of buses powers and the outputs are PDFs of system states. Therefore, the relation between the system variables over the time will be lost. To overcome this issue, analytic time series load flow (analytic TLF) is introduced in this work. TLF considers the effect of time synchronization and correlation between different loads in the network. Auto regressive moving average (ARMA) models are used to model the time varying loads and generations. The inputs in analytic TLF are ARMA model parameters of active and reactive powers of load buses and the active power of generation buses. The outputs are ARMA parameters of the voltage magnitude and phase of load buses as well as voltage phase of generation buses. The performance of the proposed analytic TLF is evaluated using several examples.