We consider a multivariate interstage dependent stochastic process whose components follow a generalized autoregressive model with time varying order. At a given time step, we give some recursive formulae linking future values of the process with past values and noises. We then consider multistage stochastic linear programs with uncertain polyhedral sets depending affinely on such processes. At each stage, when uncertainty is dealt with by means of probabilistic and CVaR constraints, the recursive relations can be used to obtain explicit expressions for the feasible set, making the corresponding risk-averse stochastic linear program tractable. Finally, we show how a rolling-horizon implementation of these risk-averse programs gives a strategy that is risk-averse, time consistent, and nonanticipative.