Simple stochastic models Rt to time series of daily precipitation amou
nt have a marked tendency to underestimate the observed (or interannua
l) variance of monthly (or seasonal) total precipitation. By consideri
ng extensions of one particular class of stochastic model known as a c
hain-dependent process, the extent to which this ''overdispersion'' ph
enomenon is attributable to an inadequate model for high-frequency var
iation of precipitation is examined. For daily precipitation amount in
January at Chico, California, fitting more complex stochastic models
greatly reduces the underestimation of the variance of monthly total p
recipitation. One source of overdispersion, the number of wet days, ca
n be completely eliminated through the use of a higher-order Markov ch
ain for daily precipitation occurrence. Nevertheless, some of the obse
rved variance remains unexplained and could possibly be attributed to
low-frequency variation (sometimes termed ''potential predictability''
). Of special interest is the fact that these more complex stochastic
models still underestimate the monthly variance, more so than does an
alternative approach, in which the simplest form of chain-dependent pr
ocess is conditioned on an index of large-scale atmospheric circulatio
n.