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*. You can choose whether the transformations are to be fixed or estimated, by specifying one string for each explanatory variable.

_{t}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*, Genstat has to make assumptions about the unknown values of

_{t}*x*which came before the observation period. The default is that

_{t}*x*(or generally

_{t}*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