Coliforms and fecal streptococcus in the Illinois River at Peoria ...

components responsible for the characteristics of
the time series. The components are the trend (T),
seasonal index (S), cyclical index (C) and irregular
movements (I). 35,36 The mathematical relationship
of the observed data (Y) to these components is
in the form:
The basic purpose of a time series analysis is to estimate
the values of T, S, C, and I.
The trend can be estimated by 1) the method of
least squares, 2) freehand method, 3) moving average
method, 4) high-low midpoint method, and 5)
the semi-average method. The seasonal index which
permits an estimate of variations during a selected
time interval within a year can be computed by 1)
the average percentage method, 2) percentage trend
(ratio of trend) method, 3) percentage moving
average (ratio to moving average) method, and 4)
the link relative method. The term CI is computed
by dividing the observed data value, for a selected
interval, by the product of the corresponding values
determined for T and S, i.e., Y/TS. The cyclical index
can be isolated from the CI term with an appropriate
moving average method, thus smoothing
out the irregular or random variations of CI values.
The irregular movement (I) is then computed by
the relationship Y/TSC.
The selected time interval for the time series
analysis was monthly; and geometric means (Mg)
for TC, FC, and FS for each month of the period
of record, in log form, were used for Y. Trend
values for each type of bacteria for each month
were computed by the five methods previously
mentioned. The least squares method in linear
form produced the best results for the Illinois River
data. The seasonal indexes were computed by the
four methods previously noted. Three of the methods,
i.e., the percentage trend, percentage moving
average, and the link relative produced comparable
results. Values derived from the percentage trend
method are reported here. Cyclical indexes were
developed from a three-month moving average, and
they did not differ significantly from 100 percent,
especially for FS. These methods suggest that the
irregular factor (I) can approximately be determined
by Y/TS. Nevertheless, I values presented
here are calculated by Y/TSC.
The trends, seasonal indexes, cyclical indexes,
and irregular movements for TC, FC, and FS are
shown in table 11. The predicted bacterial density
for any one month depicted in these tables is the
product of the trend value for that month, the seasonal
and cyclical indexes, and irregular movements,
i.e., Y = TSCI. A review of table 11 shows a general
trend of increasing total conform densities at Peoria,
the highest seasonal index occurring in January. The
trend for fecal conform densities is in a decreasing
mode though at a very slow rate. The highest seasonal
indexes occur during June, July, and September.
The trend for fecal streptococcus densities is
also in a decreasing pattern though hardly perceptible.
The higher seasonal indexes occur during
September and October.
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