BoxJenk Instruction

[ivory4]

See page 195 of the reference manual (under FREQUENCY).

AR Coeff Ph1=1.2;Phi2=-0.3
MA Coeff Theta1=-1.4, Theta2=0.5
I switch AR and MA coefficeints to get FFT of PSI(L) in yt=PSI(L)et

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frequency 1 512
compute scale=0.05^2/(2*%pi)
equation(noconstant, coeffs=||1.4,-0.5,-1.2,0.3||) arma y 2 2
trfunc(equation=arma) 1
set 1= %z(t,1)- %z(1,1)
cmult(scale=scale) 1 1
ctor 1 256
# 1
# result

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equation(noconstant, coeffs=||1.2,-0.3,-1.4,0.5||) arma y 2 2
@armaspectrum arma

it seems that these two parts are only different in terms of %z(1,1)

but I understand the procedure more
Thank you for help.


ps: %Z(t, Source)

[ivory4]

One question about convergence using Boxjenk
For example if I use @autofit with 3 lags on AR and MA part, it generates the table with AIC and BIC. But I notice that if I fit the data to ARIMA(3,1,2) using Boxjenk (maxl), actually it fails to converge.

This means that the AIC BIC are also wrong (for 3,1,2).

While I try to fit ARIMA(3,1,2) manually, with piters=@@@, pmethod=simplex, still it does not converge. However it does converge for all other combinations of 3 lags on either AR or MA part.

Is there a suggestion on this one?

[TomDoan]

Was the (3,1,2) the model that BIC chose? Probably not. The models that fail to converge are almost always overparameterized; a 3,1,2 model isn't even identified if the 2,1,1 is the correct model. Two extra parameters for no better fit means that the model wouldn't be selected anyway.

[ivory4]

Here is the file

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open data 10sum.txt"

calendar(q) 1947:1
data(format=free,org=columns) 1947:1 2009:1 lgdp
set lgdp = 100.0*lgdp
@bjautofit(diffs=1,constant,pmax=4,qmax=4,crit=aic) lgdp

AIC analysis of models for series LGDP
MA
AR 0 1 2 3 4
0 700.1402 677.1955 668.9370 669.5915 671.5895
1 669.7356 670.8260 669.9930 671.5911 673.3505
2 670.1904 671.0526 667.1592 673.9997 673.8136
3 669.4065 668.6532 660.4291* 670.9865 662.8811
4 669.3186 673.1461 672.5924 665.2340 667.1738

This low AIC (for 3,1,2) is caused by non convergence, if fit (3,1,2) even using cvcrit=0.001 as in @bjautofit and %nreg=7, not 3+3 as in @bjautofit

[TomDoan]

The low AIC cannot be caused by non-convergence; it's potentially a high AIC that's caused by that.

The 3,1,2 model is overparameterized---the convergence problem is caused by it bumping into the invertibility boundary for the MA part. But in apparently improves the fit enough that AIC prefers it over models with smaller parameter sets. BIC picks a much smaller model.

[timduy]

For this code"

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boxjenk(....,define=bjeq)
compute MAroots=%polycxroots(%eqnlagpoly(bjeq,%mvgavge))
compute ARroots=%polycxroots(%eqnlagpoly(bjeq,the dependent variable))

How does it deal with changing the start end dates? In other words, in the ARroots, the dependent variable is required. But wouldn't the time span of the dependent variable change if regression range changed?

[TomDoan]

The dependent variable in the %EQNLAGPOLY function is just a handle to the series as a symbol---it doesn't represent the data. For instance, if XX is the dependent variable, then if the equation is XX=1.0+.5*XX{1}-.3*XX{2}+U+.3*U{1} (where U is the residual), then %EQNLAGPOLY(BJEQ,XX) will be ||1.0,-.5,+.3||, which represents the polynomial 1-.5x+.3x^2

[timduy]

Duh...yeah, of course it is. Thank you.