We present a kernel auto-regressive (KA) method which can be used to represent the daily to multi-day auto-correlation structure of precipitation time series, using information both in the occurrence and intensity of measured rainfall events. The method is able to capture a larger fraction of the memory in multiple time series than commonly-used occurrence-based Markov chain models, even when the intensity distribution is allowed to be conditioned on the Markov state. The KA method is less sensitive to the spatial scale at which the data is reported, as it is not strictly reliant on patterns of wet and dry days for providing correlation. Output from the KA model can be used as weather generator model simulations, as empirical representations of process structure, as representation of weather/climate variability partitioning, or as climatological null models against which observations can be compared for statistical significance. The KA method demonstrates improvements in each of these over classic occurrence Markov chain models and daily independent climatology, in both representations of interannual precipitation variability and in downstream water balance variables. We provide climate null confidence intervals for precipitation trends (driven largely by autumn increases), and decompose variability into trend, interannual, and weather components (in increasing order of magnitude) for the Contiguous United States.