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We discuss how the ideal formalism of Computational Mechanics can be adaptedto apply to a non-infinite series of corrupted and correlated data, that istypical of most observed natural time series. Specifically, a simple filterthat removes the corruption that creates rare unphysical causal states isdemonstrated, and the new concept of effective soficity is introduced. Webelieve that Computational Mechanics cannot be applied to a noisy and finitedata series without invoking an argument based upon effective soficity. Arelated distinction between noise and randomness is also defined: Noise canonly be eliminated by increasing the length of the time series, whereas theresolution of random structure only requires the finite memory of the analysisto be increased. The benefits of these new concepts are demonstrated onsimulated times series by (a) the effective elimination of white noisecorruption from a periodic signal using the expletive filter and (b) theappearance of an effectively sofic region in the statistical complexity of abiased Poisson switch time series that is insensitive to changes in thewordlength (memory) used in the analysis. The new algorithm is then applied toanalysis of a real geomagnetic time series measured at Halley, Antarctica. Twoprincipal components in the structure are detected that are interpreted as thediurnal variation due to the rotation of the earth-based station under anelectrical current pattern that is fixed with respect to the sun-earth axis andthe random occurrence of a signature likely to be that of the magneticsubstorm. In conclusion, a hypothesis is advanced about model construction ingeneral.Comment: 46 pages (RevTeX4), 18 figures (Postscript), submitted PRE 9th  October, 200

Application of computational mechanics to the analysis of natural data: An example in geomagnetism