@GMAUTOFIT does an automatic fit of a multiplicative seasonal ARMA model to a series following the procedure described in Gomez and Maravall(2001). Note that this differs from @BJAUTOFIT as it includes multiplicative seasonal terms. It uses maximum likelihood estimation to ensure that the estimates are done over a consistent time interval. Note that it takes any differencing as given so you must decide that separately (@BJDIFF can be used to help with that)—the procedure picks the number of AR, MA, SAR and SMA parameters.

@GMAutoFit(options)  series start end

Parameters

Options

DIFF=number of regular differencings[0]

SDIFFS=number of seasonal differencings[0]

CONST/[NOCONST]

These governing the long-run behavior of the model and have to be chosen in advance.

 

REGULAR=maximum number of regular AR or MA parameters (each polynomial) [2]

SEASONAL=maximum number of seasonal AR or MA parameters (each polynomial) [1]

FULL/[NOFULL]

REGULAR and SEASONAL limit the size of each of the polynomials. By default, the search algorithm used in the description is employed. If you choose FULL, instead, an exhaustive search across the lengths of all four polynomials is done. With the default maximum lengths, FULL isn't too time-consuming (there are only 3 x 3 x 2 x 2 models, allowing for 0, 1 or 2 for each regular and 0 or 1 for each seasonal), however, with, for instance, REGULAR=3, SEASONAL=3, there are 256 combinations.

 

REPORT/[NOREPORT]

TITLE=title for report ["Search for Minimum BIC Model"]

By default, @GMAUTOFIT displays no output, so you access the information using the variables that it defines. If you use REPORT, it shows a table with all the models examined.

Description

@GMAUTOFIT searches for an approximate minimum BIC model with the maximum size of the polynomials governed by REGULAR for the AR and MA and SEASONAL for the seasonal AR and seasonal MA. Rather than attempt an exhaustive search across all four simultaneously (though you can do that with the FULL option), it first fixes the "regular" ARMA parameters at ARMA(3,0), then does an exhaustive search over the seasonal parameters only. Once those are chosen, they are fixed and an exhaustive search is done for the regular ARMA parameters.

Variables Defined

Example

This is the example file AUTOBOX.RPF.
 

cal(m) 1992:1

open data x12test.xls

data(format=xls,org=columns) 1992:1 2008:7 u11bvs

set ldata = log(u11bvs)

*

@bjdiff(diffs=2,sdiffs=1) ldata

*

@gmautofit(diffs=%%autod,sdiffs=%%autods,const=%%autoconst,report) ldata

*

boxjenk(diffs=%%autod,sdiffs=%%autods,const=%%autoconst,$

  ar=%%autop,sar=%%autops,ma=%%autoq,sma=%%autoqs,$

  outliers=standard,trace) ldata

Sample Output

This is the output from the example. It uses the Gomez-Maravall algorithm. The first block is choosing the seasonal parameters given an ARMA(3,0) for the regular parameters. The minimum BIC for that is (0,1), which is used throughout the second block which searches for the regular parameters given the seasonal ones. That (very slightly) favors ARMA(1,0) which is then used in the final block to verify that the seasonal (0,1) is best. Thus the model chosen is a multiplicative seasonal (1,1,0) x (0,1,1).

 

Search for Minimum BIC Model

Series LDATA

with 1 regular and 1 seasonal differences
 

AR MA AR(s) MA(s)    LogL     BIC

 3  0     0     0 337.1342258 -658.656431

 3  0     0     1 358.2913224 -695.766618

 3  0     1     0 351.3992627 -681.982499

 3  0     1     1 358.3995222 -690.779011

 

 0  0     0     1 355.1929371 -705.181867

 0  1     0     1 358.1785636 -705.949114

 0  2     0     1 358.1825026 -700.752985

 1  0     0     1 358.1900671 -705.972121

 1  1     0     1 358.1922743 -700.772528

 1  2     0     1 358.1805531 -695.545079

 2  0     0     1 358.2006344 -700.789249

 2  1     0     1 358.1988219 -695.581617

 2  2     0     1 358.1998579 -690.379682

 

 1  0     0     0 335.7270397 -666.250073

 1  0     0     1 358.1900671 -705.972121*

 1  0     1     0 351.1789285 -691.949844

 1  0     1     1 358.3360754 -701.060131

 

Copyright © 2025 Thomas A. Doan