Abstract A representation of a stochastic process in cannonical expansion form is introduced in this paper. A model based on these expansions is proposed for streamflow synthesis. It is shown that the proposed model not only reproduces the mean, the variance and the first-order serial correlation coefficient, but also the entire correlation-cross-correlation matrix, which implies the reproduction of total persistence. Further, it is shown that the proposed model is more parsimonious in parameters than an equivalent autoregressive model and does not require the use of a three-stage iterative procedure, viz., identification, estimation and validation, for its fitting to actual data. The model with its parameters derived from a 49-year recorded sequence, has been used to generate monthly streamflow sequences for some rivers of Punjab (India).