TRANSFERFUNCTION directive

Specifies input series and transfer function models for subsequent estimation of a model for an output series.


Option

SAVE = identifier
To name time-series save structure; default *


Parameters

SERIES = variates
Input time series

TRANSFERFUNCTION = TSMs
Transfer-function models; if omitted, model with 1 moving-average parameter, lag 0

BOXCOXMETHOD = strings
How to treat transformation parameters (fix, estimate); default fix

PRIORMETHOD = strings
How to treat prior values (fix, estimate); default fix

ARIMA = TSMs
ARIMA models for input series


Description

TRANSFERFUNCTION can be used to define input series and transfer-function models to be used by subsequent ESTIMATE statements.

   In its simplest form, when the TRANSFERFUNCTION and PRIORMETHOD parameters are unset, TRANSFERFUNCTION can be used to specify the explanatory variables for a regression with autocorrelated errors.

   The first parameter, SERIES, specifies a list of variates holding the time series of explanatory variables.

   The BOXCOXMETHOD parameter allows you to estimate separate power transformations for the explanatory variables: the variable xt is transformed to

          xt(λ) = (xtλ - 1) / λ ,                    λ ≠ 0

xt(0) = log(xt)

The default is no transformation, corresponding to xt(λ) = xt. You can choose whether the transformations are to be fixed or estimated, by specifying one string for each explanatory variable.

   The ARIMA parameter allows you to associate with each explanatory variable a univariate ARIMA model for the time-series structure of that variable. If you think such a model is inappropriate, then you should give a missing value in place of the TSM identifier, or leave this parameter unset. You can use these models in any subsequent FORECAST statement to incorporate, into the error limits of the forecasts, an allowance for uncertainties in the predicted explanatory variables; the allowance assumes that the future values of the explanatory variables are forecasts obtained using these ARIMA models.

   The TRANSFERFUNCTION and PRIORMETHOD parameters are used to define multi-input transfer-function models.

   The TRANSFERFUNCTION parameter specifies the transfer-function TSMs that are to be associated with the input series. A missing value in place of a TSM identifier causes GenStat to treat the corresponding input series as a simple explanatory variable, equivalent to a transfer-function model with orders (0,0,0,0).

   The PRIORMETHOD parameter specifies, for each input series, how GenStat is to treat the transients associated with the early values of the transfer-function response. In calculating the input component zt from the input xt, GenStat has to make assumptions about the unknown values of xt which came before the observation period. The default is that xt (or generally xt(λ)) is assumed to be equal to the reference constant c of the transfer-function model. The pattern of the transient can be controlled by introducing a number max(p+d,b+q) of nuisance parameters to represent the combined effects of all earlier input values on the observed output. Setting PRIORMETHOD=estimate specifies that these nuisance parameters are estimated so as to minimize the transients. You should, however, be careful in using this. Often all you will have to do is make a sensible choice of the reference constant c. Estimating the transients is best done as a final stage in refining the model; earlier, this may give poor numerical conditioning.

   The SAVE option allows you to name the time-series save structure created by TRANSFERFUNCTION. You can use this identifier in a later ESTIMATE statement, and eventually in a FORECAST statement. If you do not name the save structure GenStat will use the most recent save structure, which will be overwritten each time a new TRANSFERFUNCTION statement is given.

 

Option: SAVE.

Parameters: SERIES, TRANSFERFUNCTION, BOXCOXMETHOD, PRIORMETHOD, ARIMA.