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Management Science and Operations Research

14 principal claims

1. 99C22 · descriptive · principal · novelty: refutes earlier work, by the authors

   For ETS(A,N,A) with $m = 12$, $\alpha = 1.2$ and $\gamma = 0.9$, the stability condition of Section 5.4 of the ADAM monograph holds, while in the full discount recursion the effect of the initial states on the fitted values and the weight of a past observation both grow from period to period, and the largest root modulus of the cancelled MA polynomial exceeds one.

   Admissibility of lagged state space models through the ARIMA form of the whole model · entrylib:2026.000002@v3

2. 95C3 · methodological · principal · novelty: new, by the authors

   On 500 random additive ETS and GUM models, the admissibility decision from the roots of the MA polynomial after cyclotomic cancellation differed from the PBH reference on 0 models, and on the 172 models that both found inadmissible the largest mode modulus differed from the reference by at most 4.4e-13.

   Admissibility of lagged state space models through the ARIMA form of the whole model · entrylib:2026.000002@v3

3. 94C1 · descriptive · principal · novelty: new, by the authors

   With the true orders and true parameters, the MSARIMA analytic interval is calibrated over the 99 quantiles in the known-model simulation at $T$ of 100 and 300: MCE lies between 0.0007 and 0.0024 and the ratio of the interval width to the theoretical width between 0.9965 and 1.0019, with backcasting and with optimal initial states.

   Calibration of the prediction intervals of AutoMSARIMA in smooth on M1, M3, Tourism and M4 · entrylib:2026.000001@v3

4. 93C1 · descriptive · principal · novelty: refutes earlier work, by the authors

   The per-lag check accepted all 3042 ETS(A,N,A) grid models, 1482 of which do not have decaying weights, and 193 of 200 random GUM models with lags (1, 12), 10 of which do not have decaying weights.

   Admissibility of lagged state space models through the ARIMA form of the whole model · entrylib:2026.000002@v3

5. 92C26 · methodological · principal · novelty: new, by the authors

   On 1,000 further random ETS+ARIMA models, the bounds checker of adam() in R and of ADAM in Python with bounds="admissible", which run smoothEigensCpp() on the whole model, gave the same admissibility decision as the prototype check of the whole model on every model, and a penalty slope (the largest root modulus) within the bisection tolerance of it in both families.

   Admissibility of lagged state space models through the ARIMA form of the whole model · entrylib:2026.000002@v3

6. 90C24 · descriptive · principal · novelty: new, by the authors

   On 1,000 new random ADAM ETS+ARIMA models (500 with ARIMA at lag 1, 500 with seasonal ARIMA), checking the ETS part and the ARIMA polynomials apart, as adam() did with bounds="admissible", gave an admissibility decision different from the PBH reference of the whole model on about a third of the models in each family, accepting models that are not forecastable and rejecting models that are.

   Admissibility of lagged state space models through the ARIMA form of the whole model · entrylib:2026.000002@v3

7. 90C25 · methodological · principal · novelty: new, by the authors

   On the same 1,000 random ETS+ARIMA models, the check of the whole model (the MA polynomial of the ARIMA form of the whole lagged SSOE after cyclotomic cancellation, with the AR polynomial of the ARIMA part stationary), gave the same admissibility decision as the PBH reference on every model, and the same largest modulus to within rounding error on the models both found inadmissible.

   Admissibility of lagged state space models through the ARIMA form of the whole model · entrylib:2026.000002@v3

8. 88C4 · methodological · principal · novelty: new, by the authors

   On 575 random additive ETS and GUM models, including ETS models with up to two seasonal lags from {24, 168, 365} whose generator allows MA polynomial degrees up to 536, the step-down test on the MA polynomial after cyclotomic cancellation gave an admissibility decision different from the roots of that polynomial on 0 models.

   Admissibility of lagged state space models through the ARIMA form of the whole model · entrylib:2026.000002@v3

9. 88C16 · methodological · principal · novelty: new, by the authors

   On 800 random additive ETS and GUM models in four families, the implementation of the check in smooth (smoothEigensCpp() through smoothEigensR()) gave the same decision as the numpy prototype on every model, a largest root modulus within the bisection tolerance of it on the models both found inadmissible, and the same modulus and MA polynomial on three consecutive calls with each model.

   Admissibility of lagged state space models through the ARIMA form of the whole model · entrylib:2026.000002@v3

10. 83C2 · descriptive · principal · novelty: new, by the authors

    On the M4 sample, the 80% coverage of AutoMSARIMA falls with the level ratio: 0.813, 0.700 and 0.554 from the lowest to the highest of the level terciles, while ETS(MNN) of ETS forced and selected, whose error scale follows the level, covers 0.764, 0.778 and 0.814.

    Calibration of the prediction intervals of AutoMSARIMA in smooth on M1, M3, Tourism and M4 · entrylib:2026.000001@v3

11. 79C5 · descriptive · principal · novelty: new, by the authors

    On the fresh M4 sample, auto.adam error selection lowers MCE from 0.0352 to 0.0224 and the spread of 80% coverage over the level terciles from 0.272 to 0.077 against R auto.msarima (AutoMSARIMA), short of the planned reduction of MCE to 0.6 times that of auto.msarima, so the planned test is inconclusive.

    Calibration of the prediction intervals of AutoMSARIMA in smooth on M1, M3, Tourism and M4 · entrylib:2026.000001@v3

12. 78C3 · descriptive · principal · novelty: new, by the authors

    On the M4 sample, the log-normal ARIMA with the orders AutoMSARIMA selects removes the fall of 80% coverage over the level terciles (0.774, 0.783 and 0.752, a spread of 0.031) and lowers MCE from 0.0386 to 0.0177.

    Calibration of the prediction intervals of AutoMSARIMA in smooth on M1, M3, Tourism and M4 · entrylib:2026.000001@v3

13. 73C4 · descriptive · principal · novelty: new, by the authors

    On known models, the AutoMSARIMA interval of smooth 1.3.0 is calibrated no worse than that of 1.0.8 (smooth 1.0.8 and 1.3.0): at $T = 100$ in the known-model simulation its MCE is 0.0100 against 0.0120 with estimated parameters, 0.0139 against 0.0172 with selected orders and 0.0085 against 0.0246 with optimal initial states.

    Calibration of the prediction intervals of AutoMSARIMA in smooth on M1, M3, Tourism and M4 · entrylib:2026.000001@v3

14. 60C6 · interpretive · principal · novelty: new, by the authors

    The wider intervals of ETS than of AutoMSARIMA on the benchmark come from the multiplicative-error models in the ETS pool of ETS forced and selected, not from how either package computes the interval.

    Calibration of the prediction intervals of AutoMSARIMA in smooth on M1, M3, Tourism and M4 · entrylib:2026.000001@v3