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28 principal claims

41 C9 · descriptive · principal · novelty: new, by the authors
Selecting among Normal error distribution, Inverse Gaussian error distribution, Log-Normal error distribution, and Gamma error distribution in ETS(M,Md,M) via AICc achieves mean scaled pinball score (SPS), quantile bias, and quantile precision comparable to specifying the true data-generating distribution across Simulation experiment 2 synthetic series.
Staying Positive: Challenges and Solutions in Using Pure Multiplicative ETS Models · entrylib:2026.000006@v2
45 C3 · descriptive · principal · novelty: new, by the authors
For ETS(M,Md,N) simulated on Simulation experiment 1 synthetic series with an Inverse Gaussian error distribution, the percentage difference (PD) between the conditional expectation and the point forecast increases with the damping parameter $\phi$ , the trend smoothing parameter $\beta$ , the forecast horizon $h$ , the scale parameter $\sigma$ , and the level smoothing parameter $\alpha$ , with $\phi$ having the largest effect and $\alpha$ having the smallest effect among the scaled predictors.
Staying Positive: Challenges and Solutions in Using Pure Multiplicative ETS Models · entrylib:2026.000006@v2
46 C10 · descriptive · principal · novelty: new, by the authors
Across all five data-generating processes in Simulation experiment 2 synthetic series, Akram's log-ETS model achieves lower mean scaled pinball score (SPS) over the 48-step horizon than pure multiplicative ETS(M,Md,M) models with Normal error distribution, Inverse Gaussian error distribution, Log-Normal error distribution, Gamma error distribution, or AICc-selected distributions, driven by lower pinball loss in the central quantiles ( $\tau \in [0.2, 0.8]$ ) and similar performance in the distribution tails ( $\tau < 0.2$ and $\tau > 0.8$ ).
Staying Positive: Challenges and Solutions in Using Pure Multiplicative ETS Models · entrylib:2026.000006@v2
89 C10 · descriptive · principal · novelty: new, by the authors
On M4 hourly with fixed-origin evaluation, smooth TBATS is not less accurate than forecast::tbats in RMSSE beyond the non-inferiority margin of 1.05: the relative RMSSE of smooth TBATS to forecast::tbats is 0.848 (99% confidence interval 0.7969 to 0.9024).
TBATS in smooth: its formulation, and its accuracy against forecast::tbats and AutoTBATS on hourly data · entrylib:2026.000007@v2
90 C13 · descriptive · principal · novelty: new, by the authors
On M4 hourly with fixed-origin evaluation, in the Nemenyi test at level 0.99 on the per-series RMSSE of the five methods, the mean rank of smooth TBATS is lower than those of forecast::tbats and AutoTBATS by more than the critical distance of 0.3577.
TBATS in smooth: its formulation, and its accuracy against forecast::tbats and AutoTBATS on hourly data · entrylib:2026.000007@v2
90 C17 · descriptive · principal · novelty: new, by the authors
On electricity hourly with rolling-origin evaluation, in the Nemenyi test at level 0.99 on the per-series RMSSE of the five methods, the mean rank of smooth TBATS differs from those of forecast::tbats and AutoTBATS by less than the critical distance of 0.3789.
TBATS in smooth: its formulation, and its accuracy against forecast::tbats and AutoTBATS on hourly data · entrylib:2026.000007@v2
91 C4 · methodological · principal · novelty: extends earlier work, by the authors
Log-Normal error distribution, Gamma error distribution, and Inverse Gaussian error distribution distributions defined on $(0, \infty)$ can be applied directly to the multiplicative error term $(1+\epsilon_t)$ of conventional ETS(M,*,*) models without transforming the model into Akram's log-ETS model, provided $E(1+\epsilon_t)=1$ .
Staying Positive: Challenges and Solutions in Using Pure Multiplicative ETS Models · entrylib:2026.000006@v2
94 C5 · formal · principal · novelty: extends earlier work, by the authors
Concentrated log-likelihood functions for ETS(M,*,*) models under the unit-mean restriction $E(1+\epsilon_t)=1$ take closed forms for Normal error distribution $\mathcal{N}(1,\sigma^2)$ , Inverse Gaussian error distribution $\mathcal{IG}(1,\sigma^2)$ , Log-Normal error distribution $\log\mathcal{N}(-\sigma^2/2,\sigma^2)$ , and Gamma error distribution $\Gamma(\sigma^{-2},\sigma^2)$ error distributions.
Staying Positive: Challenges and Solutions in Using Pure Multiplicative ETS Models · entrylib:2026.000006@v2
94 C1 · methodological · principal · novelty: new, by the authors
smooth TBATS without ARMA is the model of De Livera TBATS: with the same smoothing parameters, damping, Box-Cox parameter and initial states, its one-step fitted values in the Box-Cox space differ from those of an independent implementation of De Livera's recursion by at most 5.1e-14 in relative terms over the 360 cases of the formulation checks.
TBATS in smooth: its formulation, and its accuracy against forecast::tbats and AutoTBATS on hourly data · entrylib:2026.000007@v2
94 C3 · methodological · principal · novelty: new, by the authors
The ARMA component of smooth TBATS is ADAM's additive ARMA component, not the ARMA errors of De Livera TBATS: for a local level with an AR(1) component, its impulse response at lags 1 to 20 differs from that of the additive component by at most 2.2e-16 and from that of ARMA errors by at least 0.01651 in each of nine pairs of smoothing parameter and AR coefficient.
TBATS in smooth: its formulation, and its accuracy against forecast::tbats and AutoTBATS on hourly data · entrylib:2026.000007@v2
96 C1 · formal · principal · novelty: extends earlier work, by the authors
In general, the conventional multi-step point forecast $\hat{y}_{t+h}$ of a pure multiplicative ETS(M,*,*) model does not coincide with the conditional arithmetic expectation $\mu_{y,t+h}$ or the conditional geometric expectation $\tilde{y}_{t+h}$ , satisfying $\hat{y}_{t+h} \le \tilde{y}_{t+h} \le \mu_{y,t+h}$ when smoothing parameters are non-zero.
Staying Positive: Challenges and Solutions in Using Pure Multiplicative ETS Models · entrylib:2026.000006@v2
100 C21 · formal · principal · novelty: new, by the authors
For a local level with a stationary ARMA part, the additive ARMA component of smooth TBATS keeps the permanent effect of a shock in the level and its transitory effect in the ARMA part, unlike the ARMA errors of De Livera TBATS that pass the persistence of the ARMA part into the level.
TBATS in smooth: its formulation, and its accuracy against forecast::tbats and AutoTBATS on hourly data · entrylib:2026.000007@v2
79 C6 · 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@v4
80 C4 · 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@v4
81 C5 · 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@v4
85 C1 · 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@v4
85 C3 · 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@v4
89 C1 · descriptive · principal · novelty: new, by the authors
Requests in the arranging and instrumentation theme make up less than 10% of MuseScore feature requests: the share of issues in theme was 0.0459 on the held-out set.
What MuseScore users ask for: unmet needs around arranging and parts · entrylib:2026.000004@v2
89 C2 · descriptive · principal · novelty: new, by the authors
Requests in the notation and engraving theme did not receive more total reactions on issues in theme than every other theme on the held-out set: they received 215 reactions, against 250 for the input, workflow and interface theme.
What MuseScore users ask for: unmet needs around arranging and parts · entrylib:2026.000004@v2
90 C2 · 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@v4
92 C4 · 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@v4
92 C16 · 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@v4
95 C1 · 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@v4
96 C24 · 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@v4
96 C25 · 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@v4
97 C3 · 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@v4
97 C22 · 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@v4
97 C26 · 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@v4