Dynamic Stochastic Models from Empirical Data (Enhanced Edition)

The word “model” is used in many situations to describe the system at hand.
Consequently, there are strong differences of opinion as to the appropriate use
of the word “model.” I t may suggest a photographic replication of the system
under study which reflects all its ramifications so that the model may adequately
represent the original system. This type of replication is seldom achieved in
practice. Every model may have a few specific purposes, such as forecasting and
control, and the model need only have just enough significant detail to satisfy
these purposes. Thus the basic premise in model building is that complicated
systems-all real systems are usually complicated-do not always need complicated
models. For instance, the complete phenomenological description of
river flow processes is very complicated. Still one can get relatively simple
models of river flow processes which yield adequate performance in forecasting
and control. Models with a degree of complexity beyond a certain level often
perform poorly in comparison with some simpler models. Often, if a model for
a given process involves a large number of parameters, it is a good indication
that we have to consider an entirely different family of models for the given
process. Thus it is advisable to fit relatively simple models to the given data and
to increase the complexity of the model only if the simpler model is not satisfactory.
In this regard, the methodology used in model building is not different
from the usual practice in other branches of science.