We introduce a general, state-space (or latent factor) model for time series and panel data. The state process has a flexible dynamics capable of approximating any Markov process arbitrarily well. It is of nite dimensional dependence, with a latent, endogenous switching regime interpretation. This latter leads to simple recursive formulas for prediction and filtering, which is generically faster than existing, simulation based methods such as the particle filter. Under some further constraints, the model can be estimated by maximum composite likelihood, with an extremely low computational cost. When applied to the stochastic volatility (SV) of asset returns, the model can capture, in a unified framework, stylized facts such as conditional skewness, volatility leverage e ect, as well as time non-reversibility. The methodology is illustrated using Apple stock data, which confirms the improvement of our model with respect to existing SV models.