Specifies input series and transfer function models for subsequent estimation of a model for an output series.
||To name time-series save structure; default *|
||Input time series|
||Transfer-function models; if omitted, model with 1 moving-average parameter, lag 0|
||How to treat transformation parameters (
||How to treat prior values (
TRANSFERFUNCTION can be used to define input series and transfer-function models to be used by subsequent
In its simplest form, when the
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.
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.
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.
PRIORMETHOD parameters are used to define multi-input transfer-function models.
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).
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.
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.
Commands for: Time series.
" 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