We present a spatio-temporal modelling framework for stochastic fields that obey exact symmetry in space and time, i.e. the field amplitude considered as a stochastic process in time at a fixed position in space is identical, as a stochastic process, to the field amplitude considered as a stochastic process in space at a fixed time point. The stochastic fields are given in explicit form and include intermittency as a basic ingredient. A causal version is discussed with respect to turbulence modelling and in relation to Taylor's Frozen Flow Hypothesis.