abnormal data

[ivory4]

This data series fits ARIMA(2,1,2) (2,1,3) (2,1,0) well but when fit to ARIMA(2,1,1),

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BOXJENK(DIFFS=1,CONST,MAXL,AR=2,MA=1) FF(860)

it shows

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Box-Jenkins - Estimation by ML Gauss-Newton
NO CONVERGENCE IN 34 ITERATIONS
LAST CRITERION WAS     NA
SUBITERATIONS LIMIT EXCEEDED. ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULT.
TRY HIGHER SUBITERATIONS LIMIT, TIGHTER CVCRIT, DIFFERENT SETTING FOR EXACTLINE OR ALPHA ON NLPAR.
RESTARTING ESTIMATION FROM LAST ESTIMATES OR DIFFERENT INITIAL GUESSES MIGHT ALSO WORK
Dependent Variable FF(860)
Quarterly Data From 1947:03 To 2009:01
Usable Observations    247      Degrees of Freedom   243
Centered R**2     0.999675      R Bar **2   0.999671
Uncentered R**2   1.000000      T x R**2     247.000
Mean of Dependent Variable      1525.3101440
Std Error of Dependent Variable   51.7851847
Standard Error of Estimate         0.9392664
Sum of Squared Residuals        214.37977560
Log Likelihood                    -333.97894
Durbin-Watson Statistic             1.917688
Q(36-3)                            36.922992
Significance Level of Q           0.29240369

    Variable                    Coeff      Std Error      T-Stat      Signif
********************************************************************************
1.  CONSTANT                      NA          0.000000      0.00000  0.00000000
2.  AR{1}                         NA          0.000000      0.00000  0.00000000
3.  AR{2}                         NA          0.000000      0.00000  0.00000000
4.  MA{1}                         NA          0.000000      0.00000  0.00000000

[TomDoan]

The Gauss-Newton algorithm appears to take a really bad early step which gets the parameters stuck on the boundary. Add PMETHOD=SIMPLEX,PITERS=5 (for instance) to clean up the guess values and it should work.