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dynamic model, that model will produce more accurate results. This is probably so
if the same number of parameters are used in both modeling processes. If this is not
a constraint, the statistical dynamics process known as co-integration can produce
more accurate results. But one can seldom determine in physical terms what aspect
of the co-integration model accounted for its accuracy; we are left with a quandary.
If we wish modeling to do more than simulate a complex process—that is, if
we want a model to help us understand how to change and improve a real-world
process—we prefer to use dynamic modeling. Statistical analysis is not involved in
optimizing the performance measures to complete the dynamic modeling process;
it is key to finding the parameters for the inputs to these models. For example, we
may use a normal distribution to describe the daily mean temperature to determine
the growth rate of bacteria in rivers or lakes throughout the course of a year. Statis-
tical analysis is essential in determining the mean and standard deviation of these
temperatures from the temperature record. Thus using statistical analysis, we com-
press years of daily temperature data into a single equation that is sufficient for our
modeling objectives.
1.4 Model Components
Model building begins, of course, with the properly focused question. Then the mod-
elers must decide on the boundaries of the system that contains the question, choose
a meaningful time horizon over which to explore system behavior, select an ap-
propriate time increment or “time step” (minutes, days, months, year, decade) for
which system change is modeled, and choose an adequate level of detail. But these
are verbal descriptions. Sooner or later the modeler must get down to the business
of actually building the model. The first step in that process is the identification of
the state variables, those variables that will indicate the status of this system through
time. These variables carry the knowledge of the system from step to step through-
out the run of the model—they are the basis for the calculation of the rest of the
variables in the model.
Generally, the two kinds of state variables are conserved and nonconserved. Ex-
amples of conserved variables are the population of an island or the water behind a
dam. They have no negative meaning. Examples of nonconserved state variables are
temperature or price, and they might take on negative values (temperature) or they
might not (price).
Control variables are the ones that directly change the state variables. They can
increase or decrease the state variables through time. Examples include birth (per
time period) or water inflow or outflow (to and from a reservoir).
Transforming or converting variables are sources of information used to change
the control variables. A transforming or converting variable might be the result of
an equation based on still other transforming variables or parameters. Birth rate,
contact rate, or mutation rate are examples of transforming variables.
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