

Transfer functions assume that the independent
variables and associated lags influence the direction and magnitude
of the forecast series. These models are said NOT to allow for
what is termed "feedback". A system is said to include feedback
if values of the input variable X depend in some fashion on the
past or current levels of the dependent variable. Vector ARIMA
models allow for this feedback process to occur. For example,
say current sales Z1(t) depends not only on previous sales Z1(t1),
but also on advertising expense in the previous period Z2(t1).
Feedback is said to exist if current advertising expense, Z2(t)
was influenced by sales in the previous period, Z1(t1). Being
able to describe the duality relationship between autoregressive
processes and moving average processes enables the forecaster
to use the autocorrelation and partial autocorrelation functions
to identify potential forms of univariate models. This is not
the case in Vector ARIMA. The vector model does not allow us to
move from the infinite representation of one process to the finite
representation of the other. Therefore, we need different tools
to help us identify these processes than what is generally used
in univarite ARIMA modeling. This tool is called a CCF.


