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TRANSFER FUNCTION MODELS

A Transfer function approach to modeling a time series is a multivariate way of modeling the various lag structures found in the data. It is similar to a distributed lag model in traditional econometrics. The transfer function model, however, makes use of the ratio between what are called Numerator and Denominator polynomials. The Numerator polynomials are the different lags of the exogoneous variables. The Denominator polynomials are the coefficients associated with lags of the forecast itself (i.e. the traditional dependent variable). Something called a Delay Factor or "dead time" is associated with the exogenous variables. This is the amount of time elapsed before the numerator polynomial begins to impact the forecasted series. The error term is modeled simultaneously as an ARMA process. Stationarity requirements hold the same for each exogenous series as in the univariate endogenous case. Difference operations must be used if the autocorrelation function of each series is to exhibit stationarity. These difference operations need not be exactly the same across all variables.

There may seem to be a close relationship between the Transfer Function models and multiple regression (OLS). At a glance, one might think that the regression models are a special case of the transfer function. However, they are quite different.