BJDIFF Procedure

@BJDIFF generates a table of Schwarz (BIC) criteria for various combinations of differencings and mean extractions, as a preliminary step in Box-Jenkins modeling. It can be used (if done carefully) to do an automated choice for the DIFFS, SDIFFS and CONSTANT options on a BOXJENK instruction.

@BJDIFF( options ) series start end

Parameters

series	series to analyze
start, end	range of series to use. By default, the defined range of series. Do not adjust these for the number of differencings.

Options

DIFF=maximum regular differencings[0]

SDIFFS=maximum seasonal differencings[0]

SPAN=seasonal span [CALENDAR seasonal]

TRANS=[NONE]/LOG/ROOT

Transformation to apply to data

WIDTH=window width for spectral smoothing [depends upon amount of data]

Description

@BJDIFF examines all combinations of 0 to DIFF regular differences, 0 to SDIFFS seasonal differences and non-zero mean or not using a common range determined by the maximum number of differencings allowed. The variance of the "stationary" part is estimated using non-parametric spectral methods and used to determine an approximate log likelihood for a particular set of differencings. This is converted into its Schwarz criterion (or BIC) where the only parameter that might be estimated is the constant.

Variables Defined

%%AUTOD	recommended number of regular differencings (INTEGER)
%%AUTODS	recommended number of seasonal differencings (INTEGER)
%%AUTOCONST	recommended choice for CONST option (INTEGER)

Example

This is the example program 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. The choice of the procedure is 1 regular, 1 seasonal, no constant, which is a common choice for seasonal data. The only close competitor is the same model with the constant.

BJDiff Table, Series LDATA

Reg Diff Seas Diff Intercept Crit

0 0 No 0.844633

0 0 Yes -5.076124

0 1 No -6.286452

0 1 Yes -6.374283

1 0 No -5.969619

1 0 Yes -5.952947

1 1 No -6.527156*

1 1 Yes -6.498573

2 0 No -5.469264

2 0 Yes -5.442213

2 1 No -6.103301

2 1 Yes -6.074705