  We discuss how the ideal formalism of Computational Mechanics can be adapted
to apply to a non-infinite series of corrupted and correlated data, that is
typical of most observed natural time series. Specifically, a simple filter
that removes the corruption that creates rare unphysical causal states is
demonstrated, and the new concept of effective soficity is introduced. We
believe that Computational Mechanics cannot be applied to a noisy and finite
data series without invoking an argument based upon effective soficity. A
related distinction between noise and randomness is also defined: Noise can
only be eliminated by increasing the length of the time series, whereas the
resolution of random structure only requires the finite memory of the analysis
to be increased. The benefits of these new concepts are demonstrated on
simulated times series by (a) the effective elimination of white noise
corruption from a periodic signal using the expletive filter and (b) the
appearance of an effectively sofic region in the statistical complexity of a
biased Poisson switch time series that is insensitive to changes in the
wordlength (memory) used in the analysis. The new algorithm is then applied to
analysis of a real geomagnetic time series measured at Halley, Antarctica. Two
principal components in the structure are detected that are interpreted as the
diurnal variation due to the rotation of the earth-based station under an
electrical current pattern that is fixed with respect to the sun-earth axis and
the random occurrence of a signature likely to be that of the magnetic
substorm. In conclusion, a hypothesis is advanced about model construction in
general.
