| Annual rainfall time series for Sydney from 1859 to 1999 is analysed. Clear
evidence of nonstationarity is presented, but substantial evidence for persistence or
hidden states is more elusive. A test of the hypothesis that a hidden state Markov model
reduces to a mixture distribution is presented. There is strong evidence of a correlation
between the annual rainfall and climate indices. Strong evidence of persistence of one of
these indices, the Pacific Decadal Oscillation (PDO), is presented together with a
demonstration that this is better modelled by fractional differencing than by a hidden
state Markov model. It is shown that conditioning the logarithm of rainfall on PDO, the
Southern Oscillation index (SOI), and their interaction provides realistic simulation of
rainfall that matches observed statistics. Similar simulation models are presented for
Brisbane, Melbourne and Perth.
Keywords: Hydrological persistence,hidden state Markov models, fractional differencing, PDO,
SOI, Australian rainfall |