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 = string tokens	How to treat transformation parameters (fix, estimate); default fix
PRIORMETHOD = string tokens	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 TFIT 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 x_t is transformed to

x_t^(λ) = (x_t^λ – 1) / λ ,                    λ ≠ 0

x_t⁽⁰⁾ = log(x_t)

The default is no transformation, corresponding to x_t^(λ) = x_t. 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 TFORECAST 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 z_t from the input x_t, Genstat has to make assumptions about the unknown values of x_t which came before the observation period. The default is that x_t (or generally x_t^(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 TFIT statement, and eventually in a TFORECAST 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.

See also

Directives: TSM, FTSM, TDISPLAY, TFILTER, TFIT, TFORECAST, TKEEP, TSUMMARIZE.

Procedures: BJESTIMATE, BJFORECAST, BJIDENTIFY.

Commands for: Time series.

Example

" Example TFIT-4: Fit a transfer-function model"

FILEREAD [NAME='%gendir%/examples/TFIT-4.DAT'; IMETHOD=read]

" Form and display the cross correlations between the two series"
CORRELATE [GRAPH=cross; MAXLAG=40] SERIES=igr; LAGGED=co2
& SERIES=co2; LAGGED=igr

" Define a transfer-function model relating the series, and
  ARIMA models for each  series"
TSM igrarma; ORDERS=!(3,0,0);\ 
   PARAMETERS=!(1.0,-0.0567,0.0353,1.97,-1.37,0.34)
TSM [MODELTYPE=transfer] igrtfm; ORDERS=!(3,1,0,2);\ 
   PARAMETERS=!(1,0,0.616881,-0.55752,0.31648,0.46259)
TSM co2arma; ORDERS=!(2,0,0); PARAMETERS=!(1,0,0.114455,1.298612,-0.442405)

" Fit the models"
TRANSFER igr; TRANSFER=igrtfm; ARIMA=igrarma
TFIT co2; TSM=co2arma