Methods of Environmental Data Analysis by A. C. Bajpai, Irene M. Calus, J. A. Fairley (auth.), C. N.

By A. C. Bajpai, Irene M. Calus, J. A. Fairley (auth.), C. N. Hewitt (eds.)

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Apart from reducing possible risk arising from round-off error, fewer digits mean fewer keys to be pressed, thus saving time and reducing opportunities of making wrong entries. In fact, the %Fe data could be even further simplified by making 0·0 I the unit, so that the values become 2,0, 5, I and 7. It would then be necessary, when s has been calculated, to convert back to the original units by multiplying by 0·01. A more detailed explanation of coding is given in Ref. 4. 5 Calculating s from a frequency table As with the arithmetic mean, calculating s from data given in the form of a frequency table is just a matter of adapting the original definition.

The approach is based around the well-known 'structural' or 'com- NONSTATIONARY TIME-SERIES ANALYSIS 49 ponent' time-series model and, like previous state-space solutions,22-24 it employs the standard Kalman filter-type l2 recursive algorithms. ) Except in the final forecasting and smoothing stages of the analysis, however, the justification for using these algorithms is not the traditional one based on 'optimality' in a prediction error or maximum likelihood (ML) sense. Rather, the algorithms outlined here are utilised in a manner which allows for straightforward and effective spectral decomposition of the time series into quasi-orthogonal components.

00085 s = 0·029 determinations of %Fe made by Laboratory B. ) Similar calculations give, for Laboratory A's results, s = 0'167, the larger value reflecting the greater amount of spread. 3 A shortcut method The formula for s can be converted into an alternative form which cuts out the step of calculating deviations from the mean. By simple algebra, it can be shown that (6) The %Fe results obtained by Laboratory B are again chosen for illustration. From Table 6, LX = 70·65 and Lx2 = 998·2879. 65 2/5 998·2879 - 998·2845 0·0034 s is then found as before.

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