ExtendedAirline model: Seasonal MA Part is eliminated for AR=true

[ChristianeHofer]

Dear @palatej ,
@webelk and I debugged the code. We have a question to the following:

jdemetra-core/demetra-highfreq/demetra-highfreq-core/src/main/java/jdplus/highfreq/ExtendedAirlineMapping.java

Lines 150 to 158 in d46dea8

	if (ar) {
	double ph = -phi.get(1);
	p[0] = ph;
	for (int i = 0; i < p0.length; ++i) {
	if (!round) {
	p[i + 1] = -theta.get(p0[i]-1) / f0[i];
	} else {
	p[i + 1] = -theta.get(p0[i]-1);
	}

Why is the index for ar=true (p0[i]-1) and ar=false (p0[i]) different?
In the case of AR=true, we put in our example
AR = 1,00000 - 0,200000 B; MA = 1,00000 - 0,200000 B^7; var =1.0
and got back 0.2 and 0 what results to the model:
AR = 1,00000 - 0,200000 B; MA = 1,00000; var =1.0.
Why is this behaviour needed?. Regards Christiane

[palatej]

Hi Christiane, you are right. I will correct the code.

To be noted that the objective of ar=true is to diminish the differencing orders that generate a lot of numerical problems.
So, with ar = true, we replace (1-B)y = (1-thetaB)e by (1-phiB)y =e. The periodic ar/ma polynomials are omitted to simplify the notations; they are the same in both models.

Not sure that I will keep that option in the final version.

[palatej]

Additional comment:
Models with stationary AR polynomials are often non decomposable, which lead to other problems (we use the "noisy" approach: we add noise in the initial model to make it decomposable; the irregular is null in that case).

[webelk]

Thank you, Jean. This information is very useful for us.