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These polynomials are of interest in that they explicitly show the
lead/lag structure between time series X and Y as revealed by the data.
Depending on the nature of X( 8), the parameters of 5(B) and X(B) may be
estimated using ordinary least squares, non-linear least squares, or
maximum likelihood techniques.
The transfer function embodies the causal properties and lead/lag
structure between X and Y and provides the basis from which to determine
the speed and magnitude with which change in X is reflected in Y, given
the specification above. In addition, the structural characteristics of
the relationship between X and Y have been supported by giving the data
a chance to speak'* of relationships that do or do not exist, comple
menting expectations based on theory and minimizing the probability of
misspecification.
Once the transfer function relating X and Y has been identified,
the lead/lag structure; e.g., current and/or lagged prices, are included
in a more complete explanatory model of the market. The regression
methods that are employed to estimate the econometric model of prices
are discussed below.
General Regression Methods
The analysis of time series properties, causality tests, and deri
vation of the transfer function provides a set of expressions in terms
of endogenous and lagged endogenous variables. These expressions evolve
into a more comprehensive model when they are augmented with additional
exogenous variables whose presence is dictated by theory and knowledge
of the market. This study strives to generate such models describing
price at each of three market levels.