Predictive simulation of time series data is useful for many applications such as risk management and stress-testing in finance or insurance, climate modeling, and electricity load forecasting. This (preprint) paper proposes a new approach to uncertainty quantification for univariate time series forecasting. This approach adapts split conformal prediction to sequential data: after training the model on a proper training set, and obtaining an inference of the residuals on a calibration set, out-of-sample predictive simulations are obtained through the use of various parametric and semi-parametric simulation methods. Empirical results on uncertainty quantification scores are presented for more than 250 time series data sets, both real world and synthetic, reproducing a wide range of time series stylized facts.