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response model which embodies the dynamic nature of the relationship
exhibited by the two time series.
Haugh and Box (1977) outline the dynamic regression procedure as a
two-step process which identifies (1) the relationship between two
series by characterizing the univariate models of each time series and
(2)the relationship between the two univariate innovation series. The
innovation series are each assumed a white noise process and are con
sidered the "driving force" of the original series. Shonkwiler and
Spreen (1982) provide a more detailed outline of the dynamic regression
procedure, which would be to
(1) identify and estimate univariate time series or filter models
for each series of interest via Box-Jenkins methodology,
(2) use the innovation series of the filtered series to determine
the properties of causality between the series via Haugh and
Pierce notions of causality,
(3) identify a "dynamic shock" model that expresses the relation
ship between the innovation series given the causal pattern
from (2) via Haugh and Box methodology, and
(4) derive an "impulse response" or distributed lag model utiliz
ing knowledge of the original univariate filter models and the
dynamic shock models via Haugh and Box methodology. This
final specification is referred to as the transfer function.
Filter Models
The filters are determined by applying time series methods to the
original time series; e.g., Xt and Yt, as discussed earlier in this
chapter. Stationary time series u^ and vt are obtained which can be
represented by
0(B)Xt = ut