QUESTION:
Please explain
INTERVENTION MODELING when I know a priori the timing and the duration of an
event.
ANSWER:
In this section, we
discuss a class of models and a model development process for time series
influenced
by identifiable isolated
events. More commonly known as intervention analysis, this type of modeling is
transfer function
modeling with a stochastic output series and a deterministic input variable.
The values
of the input variable
are usually set to either zero or one, indicating off or on. For instance, a
time series
disturbed by a single
event, such as a strike or a price change, could be modeled as a function of
its own
past values and a
"dummy" variable. The dummy input would be represented by a series of
zeroes, with a
value of one at the time
period of the intervention. A model of this form may better represent the time
series under study.
Intervention modeling can also be useful for "what if" analysis -
that is, assessing the
effect of possible
deterministic changes to a stochastic time series.
There can be flaws
associated with theory based models. It is called model specification bias and
following
is an example. Consider
the assumption of a level shift variable starting at time period T. The modeler
knows that this is the
de jure date of the intervention. For example, the date that a gun law went
into
effect. If the true
state of nature is that it took a few periods for the existence of the law to
affect the
behavior then no
noticeable effect could be measured during this period of delay. If you split
the data into
two mutually exclusive
groups based upon theory, the test results will be biased towards no difference
or
no effect. This is
because observations that the user is placing in the second group rightfully
belong in
the first group, thus
the means then are closer than otherwise and a false conclusion can arise. This
specification error has
to be traded off with the potential for finding spurious significance when
faced
with testing literally
thousands and thousands of hypothesis.