  Reliable prediction of large chaotic sytems in the short to middle time range
is of interest in a number of fields, including climate, ecology, seismology,
and economics. In this paper, results from chaos theory, and statistical theory
are combined to suggest rulse for building linear predictive models of chaotic
systems. The rules are tested on a problems identified as hard in the climate
literature, interseasonal to interannual prediction of regional seasonal
precipitation. In a test of prediction the method yields third season ahead
predictions in 4 regions over 5 seasons which beat the NOAA climate prediction
centers half season predictions for the same region and seasons. In a test
using dimensionless climate patterns to infer parameters of the climate system,
remarkably accurate estimates of increase in average global surface air
temperature are produced.
