Difference between noise in Estimate function and noise calculated with DifEq

[César Pérez Álvarez]

The follow code estimates the IPI series and shows that "difference" that is the difference between "noise" (the noise in Estimate) and "NIpi" (the noise calculated from residuals and using psi-weights) is not zero.
/
Set Include("ipi.bdt");

Serie Tri1 = CalInd(M(1), Trimestral);
Serie Tri2 = CalInd(M(4), Trimestral)-Tri1;
Serie Tri3 = CalInd(M(7), Trimestral)-Tri1;
Serie Tri4 = CalInd(M(10), Trimestral)-Tri1;
Set InpIPI = SetOfSet(InputDef(0.1, Tri2),

InputDef(0.1, Tri3),
InputDef(0.1, Tri4));

Serie IPITri = DatCh(IPI, Trimestral, SumS);

Set MDP = ModelDef(Log(IPITri), 1, 0, 4, 0, Polyn 1-B,

Polyn 1, Polyn 1 ?, Polyn 1-0.1*B, Polyn 1 ?,
InpIPI, Copy(Empty));

Set MEP = Estimate(MDP, First(IPITri), y2006);

Polyn ma = BinGroup("*", MEP[2][8]);
Polyn ari = (BinGroup("*", MEP[2][7])*MEP[2][6]);
Ration psi = ma/ari;
Serie residuals = MEP[3][1];
Serie noise = MEP[3][3];
Serie NIpi = DifEq(psi, residuals,SubSer(noise, y1992m04d01, y1992m04d01));
Serie NIpi2 = DifEq(psi, residuals,noise);
Serie difference = noise-NIpi;
/
The ipi.bdt file:
/

Mensual;IPI;
1992/01/01;81.2;
1992/02/01;82.5;
1992/03/01;83.7;
1992/04/01;81.2;
1992/05/01;84;
1992/06/01;82.9;
1992/07/01;83.2;
1992/08/01;48.3;
1992/09/01;79.7;
1992/10/01;82.7;
1992/11/01;78.9;
1992/12/01;69.4;
1993/01/01;74.4;
1993/02/01;73.6;
1993/03/01;77.3;
1993/04/01;72.8;
1993/05/01;79.7;
1993/06/01;78;
1993/07/01;79.3;
1993/08/01;45.9;
1993/09/01;78;
1993/10/01;81.3;
1993/11/01;80.6;
1993/12/01;72.8;
1994/01/01;75.3;
1994/02/01;77.7;
1994/03/01;83.3;
1994/04/01;78.7;
1994/05/01;82.9;
1994/06/01;85;
1994/07/01;86;
1994/08/01;51.7;
1994/09/01;84.1;
1994/10/01;87.4;
1994/11/01;88.3;
1994/12/01;81.9;
1995/01/01;84.7;
1995/02/01;82.9;
1995/03/01;88.9;
1995/04/01;83.7;
1995/05/01;90;
1995/06/01;90.3;
1995/07/01;88.8;
1995/08/01;54.2;
1995/09/01;86.9;
1995/10/01;88.8;
1995/11/01;89.3;
1995/12/01;80.6;
1996/01/01;81.4;
1996/02/01;81.9;
1996/03/01;86.9;
1996/04/01;81.1;
1996/05/01;87.2;
1996/06/01;89.2;
1996/07/01;88.3;
1996/08/01;54.6;
1996/09/01;86.1;
1996/10/01;90.5;
1996/11/01;89.7;
1996/12/01;78.9;
1997/01/01;85.6;
1997/02/01;83.3;
1997/03/01;94.3;
1997/04/01;87.4;
1997/05/01;91.5;
1997/06/01;94.1;
1997/07/01;95.9;
1997/08/01;60.2;
1997/09/01;93.3;
1997/10/01;98.8;
1997/11/01;95.4;
1997/12/01;85.1;
1998/01/01;91.4;
1998/02/01;93.1;
1998/03/01;97.2;
1998/04/01;92.9;
1998/05/01;98.3;
1998/06/01;99.7;
1998/07/01;100.7;
1998/08/01;62.9;
1998/09/01;96.7;
1998/10/01;101.6;
1998/11/01;99.4;
1998/12/01;89.3;
1999/01/01;95.3;
1999/02/01;92.9;
1999/03/01;98.6;
1999/04/01;93.6;
1999/05/01;99.4;
1999/06/01;101.6;
1999/07/01;104.4;
1999/08/01;65.6;
1999/09/01;100.2;
1999/10/01;103.3;
1999/11/01;103.9;
1999/12/01;93.4;
2000/01/01;98;
2000/02/01;100.2;
2000/03/01;105.9;
2000/04/01;98.4;
2000/05/01;107;
2000/06/01;106.4;
2000/07/01;107.2;
2000/08/01;70;
2000/09/01;103;
2000/10/01;104.2;
2000/11/01;107.9;
2000/12/01;95.2;
2001/01/01;98.4;
2001/02/01;98.8;
2001/03/01;104.4;
2001/04/01;96.3;
2001/05/01;106.1;
2001/06/01;105.9;
2001/07/01;104.3;
2001/08/01;72.2;
2001/09/01;101.9;
2001/10/01;105.1;
2001/11/01;102.7;
2001/12/01;89.1;
2002/01/01;97;
2002/02/01;97.9;
2002/03/01;103.5;
2002/04/01;97.8;
2002/05/01;104;
2002/06/01;103.1;
2002/07/01;106.1;
2002/08/01;71.2;
2002/09/01;102.3;
2002/10/01;108.2;
2002/11/01;105.2;
2002/12/01;90.9;
2003/01/01;98.2;
2003/02/01;99.6;
2003/03/01;105.1;
2003/04/01;100.2;
2003/05/01;104.5;
2003/06/01;105.4;
2003/07/01;108.1;
2003/08/01;71.7;
2003/09/01;102.7;
2003/10/01;109.4;
2003/11/01;106.6;
2003/12/01;92.1;
2004/01/01;97.5;
2004/02/01;101.2;
2004/03/01;108.6;
2004/04/01;101;
2004/05/01;107.4;
2004/06/01;109.1;
2004/07/01;109.9;
2004/08/01;72.8;
2004/09/01;106;
2004/10/01;107.7;
2004/11/01;108.9;
2004/12/01;92.8;
2005/01/01;98.3;
2005/02/01;100.4;
2005/03/01;109.5;
2005/04/01;101.3;
2005/05/01;107.5;
2005/06/01;109;
2005/07/01;109.3;
2005/08/01;75.1;
2005/09/01;106.2;
2005/10/01;107.6;
2005/11/01;109.9;
2005/12/01;97;
2006/01/01;101.7;
2006/02/01;103.1;
2006/03/01;111.4;
2006/04/01;102.5;

It is possible that we have a wrong re-calculate of the residuals in last step of the estimation? I observed that this behaviour it's not always the same. In other cases Estimate works well.

[Víctor de Buen Remiro]

Bug has been fixed in CVS.

Residuals resulting from likelihood evaluation method of Levinson doesn't match ARIMA differential equation with noise.

To avoid this incongruence and save forecasting problems, residuals will be changed after last iteration by differential equation result, at least until an exact and efficient Toeplitz-based method will be implemented.

Thanks to report