Environmental Engineering Reference
In-Depth Information
Quantitative methods of forecasting techniques, involve the analysis of historical
data in an attempt to predict future values of a variable of interest. Quantitative
forecasting models can be grouped into two kinds-univariate models and causal
models.
Univariate models are the common types of quantitative forecasting methods.
Such models predict future values of a time series, solely on the basis of the past
values of the time series. When using such models, historical data are analyzed in
an attempt to identify a data pattern. Then, if it will prevail in the future, this pattern
is projected into the future to produce forecasts. Univariate forecasting is therefore;
most useful when conditions are expected to remain the same. Changes, which are
functionally related to time, can be incorporated into this method.
The use of causal forecasting involves the identi
cation of other variables, which
in
ed these related variables, a
statistical model such as time series regression or transfer function analysis is used
to describe the relation between these variables and the variable to be forecasted.
The statistical relationship derived is then used to forecast the variable of interest
(Matalas 1966 ; Kisiel 1969 ).
For example, the BOD might be related to active bacteria and so on. In such a
case, BOD is referred as the dependent variable, while the other variables are
referred to as the independent variables. The analyst
uence the variable to be predicted. Having identi
'
is task is to statistically estimate
the functional relationship between the BOD and the independent variables. Having
estimated this relationship with a good degree of con
dence, it can be used to
predict the future values of the independent variables to predict the future values of
BOD (the dependent variable). These models are advantageous because they allow
us to evaluate the impact of various alternate policies.
4.4 Forecast Error
Unfortunately, all forecasting situations involve some degree of uncertainty. This
fact is recognized by including an irregular component in the description of a time
series. This term, which is referred to as an error term, is the resultant of all errors
made in the measurement, save for model choice. Given the model is correctly
chosen, its parameters estimated from the data. Then this estimated model is used
for prediction purposes. Thus, the forecast error for a particular forecast value is the
difference between its actual value when it is observed and the predicted value
obtained from the model. Let us denote an observation made at the time t by y t and
its forecast by
y t . Thus, the forecast error is given by:
e t = y t y t
ð 4 : 1 Þ
Examination of forecast errors over time can often indicate whether the fore-
casting technique, being used, does or does not match the data pattern. For example,
if a forecasting technique accurately forecasts the trend, seasonal, and cyclical
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