CLAIMSET TBATS in smooth: its formulation, and its accuracy against forecast::tbats and AutoTBATS on hourly data
licence CC-BY-4.0; contributions C1, C3, C10, C13, C17; highlights C1, C3, C13, C17, D1
declarations funding: none | competing interests: The guarantor is the author and maintainer of the smooth package whose TBATS the study evaluates.
exploration 2 questions; hypotheses 20: 12 supported, 4 inconclusive, 4 revised, 12 from exploration; tests 20: 16 supported, 4 inconclusive; runs 14: 5 confirmatory, 9 exploratory; lab record A9

DEFINITIONS
D1 [method] smooth TBATS: TBATS of the smooth package (R `tbats()`, Python `TBATS`): a linear single-source-of-error state space model of the Box-Cox transform $y_t^{(\lambda)}$ of the series, built on ADAM's state space core,
$$\begin{aligned} y_t^{(\lambda)} &= w^\top v_{t-\boldsymbol{l}} + \epsilon_t, \\ v_t &= F v_{t-\boldsymbol{l}} + g \epsilon_t, \end{aligned}$$
where $v_{t-\boldsymbol{l}}$ takes each state at its own lag. The level $l_t$ and the trend $b_t$ are those of ETS(A,N,N), ETS(A,A,N) or ETS(A,Ad,N),
$$\begin{aligned} l_t &= l_{t-1} + \phi b_{t-1} + \alpha \epsilon_t, \\ b_t &= \phi b_{t-1} + \beta \epsilon_t. \end{aligned}$$
Each harmonic $j = 1, \dots, k_i$ of each period $m_i$, with frequency $\lambda_{ij} = 2 \pi j / m_i$, is two states $v^{(ij)}_1$ and $v^{(ij)}_2$ with lags 1 and 2 in the ARIMA slot of ADAM's core,
$$\begin{aligned} u_{ij,t} &= v^{(ij)}_{1,t-1} + v^{(ij)}_{2,t-2}, \\ v^{(ij)}_{1,t} &= 2 \cos(\lambda_{ij}) \, u_{ij,t} + \gamma_{1i} \epsilon_t, \\ v^{(ij)}_{2,t} &= -u_{ij,t} + \left(\sin(\lambda_{ij}) \gamma_{2i} - \cos(\lambda_{ij}) \gamma_{1i}\right) \epsilon_t, \end{aligned}$$
so that $(1 - 2 \cos(\lambda_{ij}) B + B^2) \, u_{ij,t} = \left(\gamma_{1i} B + (\sin(\lambda_{ij}) \gamma_{2i} - \cos(\lambda_{ij}) \gamma_{1i}) B^2\right) \epsilon_t$. The measurement equation is
$$y_t^{(\lambda)} = l_{t-1} + \phi b_{t-1} + \sum_i \sum_{j=1}^{k_i} u_{ij,t} + a_t + \epsilon_t,$$
where $a_t$ is an optional ARMA component of ADAM: an additive block of states whose output enters the measurement equation, not ARMA errors. $\lambda \in [0, 1]$ is estimated by likelihood with the Jacobian of the transform. The harmonics are preselected by information criterion on a global regression of the transformed series on Fourier terms, and the trend and the ARMA orders are selected by AICc. With the default `distribution="auto"`, the structure is selected with the generalised normal distribution of $\epsilon_t$, and the closest of the normal, Laplace and S distributions to its estimated shape is then fitted on that structure. Code: R/adam-tbats.R and python/src/smooth/adam_general/core/tbats/ of the smooth repository, at the code versions the evidence names.
D2 [method] De Livera TBATS: TBATS of De Livera, Hyndman and Snyder (2011): for the Box-Cox transform $y_t^{(\lambda)}$,
$$\begin{aligned} y_t^{(\lambda)} &= l_{t-1} + \phi b_{t-1} + \sum_i \sum_{j=1}^{k_i} s^{(i)}_{j,t-1} + d_t, \\ l_t &= l_{t-1} + \phi b_{t-1} + \alpha d_t, \\ b_t &= \phi b_{t-1} + \beta d_t, \\ s^{(i)}_{j,t} &= \cos(\lambda_{ij}) s^{(i)}_{j,t-1} + \sin(\lambda_{ij}) s^{*(i)}_{j,t-1} + \gamma_{1i} d_t, \\ s^{*(i)}_{j,t} &= -\sin(\lambda_{ij}) s^{(i)}_{j,t-1} + \cos(\lambda_{ij}) s^{*(i)}_{j,t-1} + \gamma_{2i} d_t, \\ d_t &= \sum_{k=1}^{p} \varphi_k d_{t-k} + \sum_{k=1}^{q} \theta_k \epsilon_{t-k} + \epsilon_t, \end{aligned}$$
with $\lambda_{ij} = 2 \pi j / m_i$: ARMA(p, q) errors $d_t$ drive every state. [source B4]
D3 [method] forecast::tbats: The tbats() function of the R package forecast (Hyndman et al.), De Livera et al.'s TBATS with its own model selection, called with seasonal.periods = c(24, 168), single-threaded, otherwise default settings. [source B5]
D4 [method] AutoTBATS: AutoTBATS of the Python package statsforecast (Nixtla), called with season_length = [24, 168], otherwise default settings. [source B12]
D5 [method] ADAM ETS: ADAM ETS of smooth's Python port, ADAM(model='ZXZ', lags=[24, 168]) with its default settings: ETS with a daily and a weekly seasonal component selected by AICc. [source B8]
D6 [method] seasonal naive 168: Seasonal naive forecast repeating the last 168 observations (the last week) of the training sample.
D7 [data] M4 hourly: The 414 hourly series of the M4 competition (Makridakis et al., 2020), training samples of 700 or 960 observations and test samples of 48, from the Mcompetitions/M4-methods repository (Dataset/Train/Hourly-train.csv, Dataset/Test/Hourly-test.csv). [source B6]
D8 [data] M4 hourly validation split: The M4 hourly training samples with their last 48 observations held out as a validation test: fitting on observations 1..n-48 and evaluating on n-47..n; never the official test samples.
D9 [design] fixed-origin evaluation: Each method is fitted once to each training sample and forecasts h = 1..48 steps ahead from its end; no refits, no rolling origin.
D10 [variable] MASE: Mean absolute scaled error of a series over the horizon $h = 48$,
$$\mathrm{MASE} = \frac{\frac{1}{h} \sum_{j=1}^{h} |y_{n+j} - \hat y_{n+j}|}{\frac{1}{n-24} \sum_{t=25}^{n} |y_t - y_{t-24}|},$$
scaled by the in-sample mean absolute seasonal difference at lag 24, as in M4. [source B10]
D11 [variable] relative MASE: Geometric mean over series of the ratio of the [[D10:MASE]] of method A to that of method B; below 1, A is more accurate. Its 99% confidence interval is the exponential of the t-interval of the mean log ratio over series.
D12 [variable] coverage: Share of the test values of a set of series and horizons that lie inside the 95% prediction intervals of a method.
D13 [variable] elapsed time: Wall-clock seconds to fit a method to one training sample and produce its forecasts and intervals, single-threaded.
D14 [design] formulation checks: Deterministic checks of smooth TBATS against its specification, per seed: (H1) random parameters, initial states and series of 300 observations simulated by De Livera's recursion with normal errors, for the periods {24}, {7.3}, {24, 168}, {7.3, 30.4}, no/additive/damped trend and lambda in {1, 0.5, 0}, fitted by smooth TBATS with all parameters and initial states fixed; (H2) a noise-free series of 300 observations made of a random level and random harmonics of the periods 7.3 and 24, fitted with random fixed persistence and initial='backcasting'; (H3) nine random pairs of alpha in (0.05, 0.95) and |phi| in (0.05, 0.95) for a local level with AR(1), the impulse response w'F^(j-1)g at j = 1..20 read from the fitted model's matrices. Code: claimset-code/smooth-tbats/formulation_checks.py.
D15 [design] Nemenyi test: The Nemenyi test as computed by greybox's rmcb (distribution 'tukey', ties averaged): the methods are ranked within each series by the error measure, and two methods differ at level $1 - \alpha$ when their mean ranks over series differ by more than the critical distance
$$\mathrm{CD} = \frac{q_{1-\alpha}(k, \infty)}{\sqrt{2}} \sqrt{\frac{k (k + 1)}{6 N}}$$
for $k$ methods and $N$ series. [source B11]
D16 [variable] RMSSE: Root mean squared scaled error of a series over the horizon $h = 48$,
$$\mathrm{RMSSE} = \sqrt{\frac{\frac{1}{h} \sum_{j=1}^{h} (y_{n+j} - \hat y_{n+j})^2}{\frac{1}{n-1} \sum_{t=2}^{n} (y_t - y_{t-1})^2}},$$
scaled by the in-sample root mean squared first difference of the fitting sample, as in M5. [source B7]
D17 [variable] relative RMSSE: Geometric mean over series of the ratio of the [[D16:RMSSE]] of method A to that of method B; below 1, A is more accurate. Its 99% confidence interval is the exponential of the t-interval of the mean log ratio over series.
D18 [data] electricity hourly: The 370 hourly series of electricity consumption (kW) of clients of a Portuguese utility in GluonTS's electricity_nips archive (SR3), drawn from UCI ElectricityLoadDiagrams20112014: each series is the archive's training series extended by its last test window, ending 2014-09-08 01:00, 1249 to 6001 hours long. [source B9]
D19 [design] rolling-origin evaluation: Seven daily forecast origins over the last week of each series: the last one 48 hours before its end, the others 24, 48, ..., 144 hours earlier. At each origin each method is fitted to the 1008 preceding hours (six weeks) and forecasts 48 hours ahead; the RMSSE and the interval coverage of a series are averaged over its seven origins.
D20 [method] smooth TBATS dnorm: [[D1:smooth TBATS]] with the normal distribution of $\epsilon_t$: `TBATS(lags=[1, 24, 168], distribution="dnorm")` of the Python smooth package, every other setting at its default. The structure is selected and fitted with the normal distribution only, instead of the generalised normal distribution followed by the closest named distribution of the default `distribution="auto"`. [a kind of D1]

CLAIMS
C1 [methodological; principal; support: simulation E1 (E1.R1) artefacts A10; strength high (author); verifiability open; planning confirmatory; outcome supported]
  [[D1:smooth TBATS]] without ARMA is the model of [[D2: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 [[D14:formulation checks]].
  scope: data_type: simulated series | conditions: seeds 101 to 110; series of 300 observations; periods 24, 7.3, 168 and 30.4; Box-Cox parameter 1, 0.5 and 0; no, additive and damped trend
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  test: deterministic; tolerance 1e-08; refutation 1e-06; machine_tolerance 1e-12; sample 10 seeds (101-110), one run, no stopping rule; the checks are deterministic given the seeds; supported if h1 < tolerance; not supported if h1 >= refutation; verdict computed; flags code_changed_after_plan
  plan: lab plan PL1; planned 2026-11-11T13:16:58Z; anchor git_remote
C3 [methodological; principal; support: simulation E1 (E1.R3, E1.R4) artefacts A10; strength high (author); verifiability open; planning confirmatory; outcome supported]
  The ARMA component of [[D1:smooth TBATS]] is ADAM's additive ARMA component, not the ARMA errors of [[D2: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.
  scope: data_type: fitted models with fixed parameters | conditions: a local level with an AR(1) component; nine random pairs of smoothing parameter in (0.05, 0.95) and |AR coefficient| in (0.05, 0.95); impulse response at lags 1 to 20
  contradicts B4: De Livera, Hyndman and Snyder's TBATS has ARMA errors that drive every state; the ARMA of smooth's TBATS is an additive component of ADAM, so the two models differ whenever ARMA orders are used.
  test: deterministic; tolerance 1e-08; refutation 1e-06; machine_tolerance 1e-12; sample 10 seeds (101-110), one run, no stopping rule; the checks are deterministic given the seeds; supported if h3_adam < machine_tolerance and h3_errors > refutation; not supported if h3_adam >= refutation or h3_errors <= machine_tolerance; verdict computed; flags code_changed_after_plan
  plan: lab plan PL1; planned 2026-11-11T13:16:58Z; anchor git_remote
C10 [descriptive; principal; support: empirical_quant E3 (E3.R1, E3.T3.r1) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D7:M4 hourly]] with [[D9:fixed-origin evaluation]], [[D1:smooth TBATS]] is not less accurate than [[D3:forecast::tbats]] in [[D16:RMSSE]] beyond the non-inferiority margin of 1.05: the [[D17:relative RMSSE]] of smooth TBATS to forecast::tbats is 0.848 (99% confidence interval 0.7969 to 0.9024).
  scope: data_type: the 414 hourly series of the M4 competition | conditions: one fixed origin per series: the M4 test split; horizon 48; periods 24 and 168; smooth (Python port) at the commit of the run; comparator: forecast::tbats; measure: RMSSE
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of RMSSE (H10-H12), H0: mean log ratio >= log(1.05) against forecast::tbats and AutoTBATS (H10, H11), >= 0 against seasonal naive 168 (H12); their intervals are 99% t-intervals. H13: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series RMSSE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four one-sided t-tests the script computes (H10-H12 and the elapsed time against forecast::tbats, reported but not deciding here); the Nemenyi test's own control for H13; margin 1.05; sample All 414 series of the official M4 hourly test split, fixed by the data set; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio is 0.015, so a true relative RMSSE of 1 lies 3.3 standard errors below the non-inferiority margin log(1.05).; supported if p_ftbats < alpha; not supported if lower_ftbats > margin; verdict computed; flags code_changed_after_plan
  plan: lab plan PL5; planned 2026-11-12T00:02:39Z; anchor git_remote
C13 [descriptive; principal; support: empirical_quant E3 (E3.T1.r1, E3.T1.r2, E3.T1.r3, E3.R6) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D7:M4 hourly]] with [[D9:fixed-origin evaluation]], in the [[D15:Nemenyi test]] at level 0.99 on the per-series [[D16:RMSSE]] of the five methods, the mean rank of [[D1:smooth TBATS]] is lower than those of [[D3:forecast::tbats]] and [[D4:AutoTBATS]] by more than the critical distance of 0.3577.
  scope: data_type: the 414 hourly series of the M4 competition | conditions: one fixed origin per series: the M4 test split; horizon 48; periods 24 and 168; smooth (Python port) at the commit of the run; the five methods ranked within each series
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of RMSSE (H10-H12), H0: mean log ratio >= log(1.05) against forecast::tbats and AutoTBATS (H10, H11), >= 0 against seasonal naive 168 (H12); their intervals are 99% t-intervals. H13: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series RMSSE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four one-sided t-tests the script computes (H10-H12 and the elapsed time against forecast::tbats, reported but not deciding here); the Nemenyi test's own control for H13; margin 1.05; sample All 414 series of the official M4 hourly test split, fixed by the data set; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio is 0.015, so a true relative RMSSE of 1 lies 3.3 standard errors below the non-inferiority margin log(1.05).; supported if rank_ftbats - rank_smooth > cd and rank_autotbats - rank_smooth > cd; not supported if rank_smooth - rank_ftbats > cd or rank_smooth - rank_autotbats > cd; verdict computed; flags code_changed_after_plan
  plan: lab plan PL5; planned 2026-11-12T00:02:39Z; anchor git_remote
C17 [descriptive; principal; support: empirical_quant E4 (E4.T1.r1, E4.T1.r2, E4.T1.r3, E4.R6) artefacts A8; verifiability open; planning confirmatory; outcome inconclusive]
  On [[D18:electricity hourly]] with [[D19:rolling-origin evaluation]], in the [[D15:Nemenyi test]] at level 0.99 on the per-series [[D16:RMSSE]] of the five methods, the mean rank of [[D1:smooth TBATS]] differs from those of [[D3:forecast::tbats]] and [[D4:AutoTBATS]] by less than the critical distance of 0.3789.
  scope: data_type: 370 hourly electricity series of clients of one Portuguese utility, 2011-2014 | conditions: 7 daily origins in the last week of each series, ending 2014-09-08; 1008-hour fitting windows; horizon 48; periods 24 and 168; the five methods ranked within each series
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  qualifies C13
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of RMSSE, H0: mean log ratio >= 0, against forecast::tbats (H18), AutoTBATS (H19) and seasonal naive 168 (H16); their intervals are 99% t-intervals. H17: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series RMSSE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four one-sided t-tests the script computes (H18, H19, H16 and the elapsed time against forecast::tbats, reported but not deciding here); the Nemenyi test's own control for H17; sample All 370 series of the electricity data (TM19) less those whose RMSSE is undefined (a constant fitting window; a data check before any method was run found series 322 constant in its windows), fixed by the data set; each series' RMSSE is its mean over the 7 origins; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio over 369 series is 0.016, so a true relative RMSSE of 0.95 lies 3.3 standard errors below 1 and is detected at alpha = 0.01 (one-sided, before Holm) with probability about 0.8.; supported if rank_ftbats - rank_smooth > cd and rank_autotbats - rank_smooth > cd; not supported if rank_smooth - rank_ftbats > cd or rank_smooth - rank_autotbats > cd; verdict computed; flags code_changed_after_plan
  plan: lab plan PL7; planned 2026-11-12T10:23:25Z; anchor git_remote
C2 [methodological; secondary; not_applicable; support: simulation E1 (E1.R2) artefacts A10; verifiability open; planning confirmatory; outcome supported]
  Backcasting the initial states through the harmonic block of [[D1:smooth TBATS]] is exact: on noise-free series made of a level and harmonics, the largest absolute in-sample error over the 10 series of the [[D14:formulation checks]] is 1.8e-9.
  scope: data_type: simulated noise-free series | conditions: seeds 101 to 110; series of 300 observations; a level and harmonics of the periods 7.3 and 24
  test: deterministic; tolerance 1e-08; refutation 1e-06; machine_tolerance 1e-12; sample 10 seeds (101-110), one run, no stopping rule; the checks are deterministic given the seeds; supported if h2 < tolerance; not supported if h2 >= refutation; verdict computed; flags code_changed_after_plan
  plan: lab plan PL1; planned 2026-11-11T13:16:58Z; anchor git_remote
C4 [descriptive; secondary; support: empirical_quant E2 (E2.R1, E2.T3.r1) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D7:M4 hourly]] with [[D9:fixed-origin evaluation]], [[D1:smooth TBATS]] is not less accurate than [[D3:forecast::tbats]] in [[D10:MASE]] beyond the non-inferiority margin of 1.05: the [[D11:relative MASE]] of smooth TBATS to forecast::tbats is 0.8318 (99% confidence interval 0.7793 to 0.8877).
  scope: data_type: the 414 hourly series of the M4 competition | conditions: one fixed origin per series: the M4 test split; horizon 48; periods 24 and 168; smooth (Python port) at the commit of the run; comparator: forecast::tbats; measure: MASE
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  supports C10
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of MASE (H4-H6) or elapsed time (H7), H0: mean log ratio >= log(1.05) against forecast::tbats and AutoTBATS (H4, H5), >= 0 against seasonal naive 168 (H6) and for the time (H7); their intervals are 99% t-intervals. H9: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series MASE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four t-tests of H4-H7; the Nemenyi test's own control for H9; margin 1.05; coverage_threshold 0.9; sample All 414 series of the official M4 hourly test split, fixed by the data set; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio is 0.015, so a true relative MASE of 1 lies 3.3 standard errors below the non-inferiority margin log(1.05).; supported if p_ftbats < alpha; not supported if lower_ftbats > margin; verdict computed; flags holdout_used_elsewhere
  plan: lab plan PL3; planned 2026-11-11T13:46:12Z; anchor git_remote
C5 [descriptive; secondary; support: empirical_quant E2 (E2.R2, E2.T3.r2) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D7:M4 hourly]] with [[D9:fixed-origin evaluation]], [[D1:smooth TBATS]] is not less accurate than [[D4:AutoTBATS]] in [[D10:MASE]] beyond the non-inferiority margin of 1.05: the [[D11:relative MASE]] of smooth TBATS to AutoTBATS is 0.7803 (99% confidence interval 0.7242 to 0.8407).
  scope: data_type: the 414 hourly series of the M4 competition | conditions: one fixed origin per series: the M4 test split; horizon 48; periods 24 and 168; smooth (Python port) at the commit of the run; comparator: AutoTBATS
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  supports C11
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of MASE (H4-H6) or elapsed time (H7), H0: mean log ratio >= log(1.05) against forecast::tbats and AutoTBATS (H4, H5), >= 0 against seasonal naive 168 (H6) and for the time (H7); their intervals are 99% t-intervals. H9: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series MASE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four t-tests of H4-H7; the Nemenyi test's own control for H9; margin 1.05; coverage_threshold 0.9; sample All 414 series of the official M4 hourly test split, fixed by the data set; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio is 0.015, so a true relative MASE of 1 lies 3.3 standard errors below the non-inferiority margin log(1.05).; supported if p_autotbats < alpha; not supported if lower_autotbats > margin; verdict computed; flags holdout_used_elsewhere
  plan: lab plan PL3; planned 2026-11-11T13:46:12Z; anchor git_remote
C6 [descriptive; secondary; support: empirical_quant E2 (E2.R4, E2.T3.r3) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D7:M4 hourly]] with [[D9:fixed-origin evaluation]], [[D1:smooth TBATS]] is more accurate in [[D10:MASE]] than [[D6:seasonal naive 168]]: the [[D11:relative MASE]] of smooth TBATS to seasonal naive 168 is 0.5067 (99% confidence interval 0.4479 to 0.5734).
  scope: data_type: the 414 hourly series of the M4 competition | conditions: one fixed origin per series: the M4 test split; horizon 48; periods 24 and 168; smooth (Python port) at the commit of the run; comparator: seasonal naive 168
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  supports C12
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of MASE (H4-H6) or elapsed time (H7), H0: mean log ratio >= log(1.05) against forecast::tbats and AutoTBATS (H4, H5), >= 0 against seasonal naive 168 (H6) and for the time (H7); their intervals are 99% t-intervals. H9: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series MASE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four t-tests of H4-H7; the Nemenyi test's own control for H9; margin 1.05; coverage_threshold 0.9; sample All 414 series of the official M4 hourly test split, fixed by the data set; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio is 0.015, so a true relative MASE of 1 lies 3.3 standard errors below the non-inferiority margin log(1.05).; supported if p_snaive < alpha; not supported if lower_snaive >= 1; verdict computed; flags holdout_used_elsewhere
  plan: lab plan PL3; planned 2026-11-11T13:46:12Z; anchor git_remote
C7 [descriptive; secondary; support: empirical_quant E2 (E2.R5, E2.T3.r4) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D7:M4 hourly]], [[D1:smooth TBATS]] takes less [[D13:elapsed time]] per series than [[D3:forecast::tbats]]: the geometric mean over series of the ratio of their elapsed times is 0.5791 (99% confidence interval 0.539 to 0.6222).
  scope: data_type: the 414 hourly series of the M4 competition | conditions: one fixed origin per series: the M4 test split; horizon 48; periods 24 and 168; smooth (Python port) at the commit of the run; comparator: forecast::tbats; measure: elapsed time
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of MASE (H4-H6) or elapsed time (H7), H0: mean log ratio >= log(1.05) against forecast::tbats and AutoTBATS (H4, H5), >= 0 against seasonal naive 168 (H6) and for the time (H7); their intervals are 99% t-intervals. H9: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series MASE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four t-tests of H4-H7; the Nemenyi test's own control for H9; margin 1.05; coverage_threshold 0.9; sample All 414 series of the official M4 hourly test split, fixed by the data set; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio is 0.015, so a true relative MASE of 1 lies 3.3 standard errors below the non-inferiority margin log(1.05).; supported if p_time < alpha; not supported if lower_time >= 1; verdict computed; flags holdout_used_elsewhere
  plan: lab plan PL3; planned 2026-11-11T13:46:12Z; anchor git_remote
C8 [descriptive; secondary; support: empirical_quant E2 (E2.T1.r1) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D7:M4 hourly]], the 95% prediction intervals of [[D1:smooth TBATS]] have a [[D12:coverage]] of 0.9273, above the threshold of 0.9 the plan set.
  scope: data_type: the 414 hourly series of the M4 competition | conditions: one fixed origin per series: the M4 test split; horizon 48; periods 24 and 168; smooth (Python port) at the commit of the run; nominal level 0.95
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  test: deterministic; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of MASE (H4-H6) or elapsed time (H7), H0: mean log ratio >= log(1.05) against forecast::tbats and AutoTBATS (H4, H5), >= 0 against seasonal naive 168 (H6) and for the time (H7); their intervals are 99% t-intervals. H9: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series MASE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four t-tests of H4-H7; the Nemenyi test's own control for H9; margin 1.05; coverage_threshold 0.9; sample All 414 series of the official M4 hourly test split, fixed by the data set; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio is 0.015, so a true relative MASE of 1 lies 3.3 standard errors below the non-inferiority margin log(1.05).; supported if coverage >= coverage_threshold; not supported if coverage < coverage_threshold; verdict computed; flags holdout_used_elsewhere
  plan: lab plan PL3; planned 2026-11-11T13:46:12Z; anchor git_remote
C9 [descriptive; secondary; support: empirical_quant E2 (E2.T1.r1, E2.T1.r2, E2.T1.r3, E2.R6) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D7:M4 hourly]] with [[D9:fixed-origin evaluation]], in the [[D15:Nemenyi test]] at level 0.99 on the per-series [[D10:MASE]] of the five methods, the mean rank of [[D1:smooth TBATS]] is lower than those of [[D3:forecast::tbats]] and [[D4:AutoTBATS]] by more than the critical distance of 0.3577.
  scope: data_type: the 414 hourly series of the M4 competition | conditions: one fixed origin per series: the M4 test split; horizon 48; periods 24 and 168; smooth (Python port) at the commit of the run; the five methods ranked within each series
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  supports C13
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of MASE (H4-H6) or elapsed time (H7), H0: mean log ratio >= log(1.05) against forecast::tbats and AutoTBATS (H4, H5), >= 0 against seasonal naive 168 (H6) and for the time (H7); their intervals are 99% t-intervals. H9: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series MASE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four t-tests of H4-H7; the Nemenyi test's own control for H9; margin 1.05; coverage_threshold 0.9; sample All 414 series of the official M4 hourly test split, fixed by the data set; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio is 0.015, so a true relative MASE of 1 lies 3.3 standard errors below the non-inferiority margin log(1.05).; supported if rank_ftbats - rank_smooth > cd and rank_autotbats - rank_smooth > cd; not supported if rank_smooth - rank_ftbats > cd or rank_smooth - rank_autotbats > cd; verdict computed; flags holdout_used_elsewhere
  plan: lab plan PL3; planned 2026-11-11T13:46:12Z; anchor git_remote
C11 [descriptive; secondary; support: empirical_quant E3 (E3.R2, E3.T3.r2) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D7:M4 hourly]] with [[D9:fixed-origin evaluation]], [[D1:smooth TBATS]] is not less accurate than [[D4:AutoTBATS]] in [[D16:RMSSE]] beyond the non-inferiority margin of 1.05: the [[D17:relative RMSSE]] of smooth TBATS to AutoTBATS is 0.7959 (99% confidence interval 0.7411 to 0.8549).
  scope: data_type: the 414 hourly series of the M4 competition | conditions: one fixed origin per series: the M4 test split; horizon 48; periods 24 and 168; smooth (Python port) at the commit of the run; comparator: AutoTBATS
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  supports C13
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of RMSSE (H10-H12), H0: mean log ratio >= log(1.05) against forecast::tbats and AutoTBATS (H10, H11), >= 0 against seasonal naive 168 (H12); their intervals are 99% t-intervals. H13: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series RMSSE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four one-sided t-tests the script computes (H10-H12 and the elapsed time against forecast::tbats, reported but not deciding here); the Nemenyi test's own control for H13; margin 1.05; sample All 414 series of the official M4 hourly test split, fixed by the data set; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio is 0.015, so a true relative RMSSE of 1 lies 3.3 standard errors below the non-inferiority margin log(1.05).; supported if p_autotbats < alpha; not supported if lower_autotbats > margin; verdict computed; flags code_changed_after_plan
  plan: lab plan PL5; planned 2026-11-12T00:02:39Z; anchor git_remote
C12 [descriptive; secondary; support: empirical_quant E3 (E3.R4, E3.T3.r3) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D7:M4 hourly]] with [[D9:fixed-origin evaluation]], [[D1:smooth TBATS]] is more accurate in [[D16:RMSSE]] than [[D6:seasonal naive 168]]: the [[D17:relative RMSSE]] of smooth TBATS to seasonal naive 168 is 0.5358 (99% confidence interval 0.4785 to 0.6001).
  scope: data_type: the 414 hourly series of the M4 competition | conditions: one fixed origin per series: the M4 test split; horizon 48; periods 24 and 168; smooth (Python port) at the commit of the run; comparator: seasonal naive 168
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of RMSSE (H10-H12), H0: mean log ratio >= log(1.05) against forecast::tbats and AutoTBATS (H10, H11), >= 0 against seasonal naive 168 (H12); their intervals are 99% t-intervals. H13: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series RMSSE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four one-sided t-tests the script computes (H10-H12 and the elapsed time against forecast::tbats, reported but not deciding here); the Nemenyi test's own control for H13; margin 1.05; sample All 414 series of the official M4 hourly test split, fixed by the data set; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio is 0.015, so a true relative RMSSE of 1 lies 3.3 standard errors below the non-inferiority margin log(1.05).; supported if p_snaive < alpha; not supported if lower_snaive >= 1; verdict computed; flags code_changed_after_plan
  plan: lab plan PL5; planned 2026-11-12T00:02:39Z; anchor git_remote
C14 [descriptive; secondary; support: empirical_quant E4 (E4.R1, E4.T3.r1) artefacts A8; verifiability open; planning confirmatory; outcome inconclusive]
  On [[D18:electricity hourly]] with [[D19:rolling-origin evaluation]], [[D1:smooth TBATS]] is not shown to be more accurate than [[D3:forecast::tbats]] at level 0.99: the [[D17:relative RMSSE]] of smooth TBATS to forecast::tbats is 0.9753 (99% confidence interval 0.947 to 1.004).
  scope: data_type: 370 hourly electricity series of clients of one Portuguese utility, 2011-2014 | conditions: 7 daily origins in the last week of each series, ending 2014-09-08; 1008-hour fitting windows; horizon 48; periods 24 and 168; comparator: forecast::tbats
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  qualifies C10
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of RMSSE, H0: mean log ratio >= 0, against forecast::tbats (H18), AutoTBATS (H19) and seasonal naive 168 (H16); their intervals are 99% t-intervals. H17: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series RMSSE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four one-sided t-tests the script computes (H18, H19, H16 and the elapsed time against forecast::tbats, reported but not deciding here); the Nemenyi test's own control for H17; sample All 370 series of the electricity data (TM19) less those whose RMSSE is undefined (a constant fitting window; a data check before any method was run found series 322 constant in its windows), fixed by the data set; each series' RMSSE is its mean over the 7 origins; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio over 369 series is 0.016, so a true relative RMSSE of 0.95 lies 3.3 standard errors below 1 and is detected at alpha = 0.01 (one-sided, before Holm) with probability about 0.8.; supported if p_ftbats < alpha; not supported if lower_ftbats >= 1; verdict computed; flags code_changed_after_plan
  plan: lab plan PL7; planned 2026-11-12T10:23:25Z; anchor git_remote
C15 [descriptive; secondary; support: empirical_quant E4 (E4.R2, E4.T3.r2) artefacts A8; verifiability open; planning confirmatory; outcome inconclusive]
  On [[D18:electricity hourly]] with [[D19:rolling-origin evaluation]], [[D1:smooth TBATS]] is not shown to be more accurate than [[D4:AutoTBATS]] at level 0.99: the [[D17:relative RMSSE]] of smooth TBATS to AutoTBATS is 0.9909 (99% confidence interval 0.9753 to 1.007).
  scope: data_type: 370 hourly electricity series of clients of one Portuguese utility, 2011-2014 | conditions: 7 daily origins in the last week of each series, ending 2014-09-08; 1008-hour fitting windows; horizon 48; periods 24 and 168; comparator: AutoTBATS
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  qualifies C11
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of RMSSE, H0: mean log ratio >= 0, against forecast::tbats (H18), AutoTBATS (H19) and seasonal naive 168 (H16); their intervals are 99% t-intervals. H17: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series RMSSE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four one-sided t-tests the script computes (H18, H19, H16 and the elapsed time against forecast::tbats, reported but not deciding here); the Nemenyi test's own control for H17; sample All 370 series of the electricity data (TM19) less those whose RMSSE is undefined (a constant fitting window; a data check before any method was run found series 322 constant in its windows), fixed by the data set; each series' RMSSE is its mean over the 7 origins; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio over 369 series is 0.016, so a true relative RMSSE of 0.95 lies 3.3 standard errors below 1 and is detected at alpha = 0.01 (one-sided, before Holm) with probability about 0.8.; supported if p_autotbats < alpha; not supported if lower_autotbats >= 1; verdict computed; flags code_changed_after_plan
  plan: lab plan PL7; planned 2026-11-12T10:23:25Z; anchor git_remote
C16 [descriptive; secondary; support: empirical_quant E4 (E4.R4, E4.T3.r3) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D18:electricity hourly]] with [[D19:rolling-origin evaluation]], [[D1:smooth TBATS]] is more accurate than [[D6:seasonal naive 168]]: the [[D17:relative RMSSE]] of smooth TBATS to seasonal naive 168 is 0.8244 (99% confidence interval 0.7981 to 0.8515).
  scope: data_type: 370 hourly electricity series of clients of one Portuguese utility, 2011-2014 | conditions: 7 daily origins in the last week of each series, ending 2014-09-08; 1008-hour fitting windows; horizon 48; periods 24 and 168; comparator: seasonal naive 168
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  supports C12
  test: frequentist; alpha 0.01; test one-sided one-sample t-test on the per-series log ratios (smooth TBATS over the comparator) of RMSSE, H0: mean log ratio >= 0, against forecast::tbats (H18), AutoTBATS (H19) and seasonal naive 168 (H16); their intervals are 99% t-intervals. H17: the Nemenyi test (greybox rmcb, distribution='tukey', level 0.99, ranks averaged over ties) on the per-series RMSSE of the five methods, with its own family-wise control over the pairwise comparisons (not in the Holm family); sides less; correction holm over the four one-sided t-tests the script computes (H18, H19, H16 and the elapsed time against forecast::tbats, reported but not deciding here); the Nemenyi test's own control for H17; sample All 370 series of the electricity data (TM19) less those whose RMSSE is undefined (a constant fitting window; a data check before any method was run found series 322 constant in its windows), fixed by the data set; each series' RMSSE is its mean over the 7 origins; one run, no interim analysis. For orientation: with a standard deviation of the per-series log ratio of 0.3, the standard error of the mean log ratio over 369 series is 0.016, so a true relative RMSSE of 0.95 lies 3.3 standard errors below 1 and is detected at alpha = 0.01 (one-sided, before Holm) with probability about 0.8.; supported if p_snaive < alpha; not supported if lower_snaive >= 1; verdict computed; flags code_changed_after_plan
  plan: lab plan PL7; planned 2026-11-12T10:23:25Z; anchor git_remote
C18 [descriptive; secondary; support: empirical_quant E5 (E5.R1, E5.T3.r1) artefacts A8; verifiability open; planning confirmatory; outcome inconclusive]
  On [[D18:electricity hourly]] with [[D19:rolling-origin evaluation]], [[D20:smooth TBATS dnorm]] is not shown to be less accurate than [[D1:smooth TBATS]] with its default distribution: the [[D17:relative RMSSE]] of smooth TBATS dnorm to smooth TBATS is 0.9275 (99% confidence interval 0.7825 to 1.099).
  scope: data_type: 370 hourly electricity series of clients of one Portuguese utility, 2011-2014 | conditions: 7 daily origins in the last week of each series, ending 2014-09-08; 1008-hour fitting windows; horizon 48; periods 24 and 168; comparator: smooth TBATS
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  qualifies C19
  test: frequentist; alpha 0.01; test one-sided one-sample t-tests over series on the per-series means over the 7 origins: H20, the log ratio of RMSSE, smooth TBATS (auto) over smooth TBATS dnorm, H0: mean >= 0; H21, the coverage of the 95% interval of smooth TBATS dnorm minus 0.95, H0: mean >= 0; H22, the log ratio of the elapsed time, smooth TBATS dnorm over smooth TBATS (auto), H0: mean >= 0. Intervals are 99% t-intervals; relative RMSSE and relative elapsed time (dnorm over auto) are the exponentials of the mean log ratios and their intervals; sides less; correction holm over the three t-tests (H20, H21, H22); sample All 370 series of the electricity data (TM19) less those whose RMSSE is undefined (series 322 in RN13) and, per test, those with a non-finite value; fixed by the data set; one run, no interim analysis; supported if p_rmsse < alpha; not supported if up_rmsse <= 1; verdict computed
  plan: lab plan PL8; planned 2026-11-13T10:26:26Z; anchor git_remote
C19 [descriptive; secondary; support: empirical_quant E5 (E5.R3, E5.T1.r2, E5.T3.r2) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D18:electricity hourly]] with [[D19:rolling-origin evaluation]], the 95% prediction intervals of [[D20:smooth TBATS dnorm]] cover fewer test values than the nominal level: their mean [[D12:coverage]] minus 0.95 is -0.0168 (99% confidence interval -0.02364 to -0.009956).
  scope: data_type: 370 hourly electricity series of clients of one Portuguese utility, 2011-2014 | conditions: 7 daily origins in the last week of each series, ending 2014-09-08; 1008-hour fitting windows; horizon 48; periods 24 and 168; nominal level 0.95
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  qualifies C20
  test: frequentist; alpha 0.01; test one-sided one-sample t-tests over series on the per-series means over the 7 origins: H20, the log ratio of RMSSE, smooth TBATS (auto) over smooth TBATS dnorm, H0: mean >= 0; H21, the coverage of the 95% interval of smooth TBATS dnorm minus 0.95, H0: mean >= 0; H22, the log ratio of the elapsed time, smooth TBATS dnorm over smooth TBATS (auto), H0: mean >= 0. Intervals are 99% t-intervals; relative RMSSE and relative elapsed time (dnorm over auto) are the exponentials of the mean log ratios and their intervals; sides less; correction holm over the three t-tests (H20, H21, H22); sample All 370 series of the electricity data (TM19) less those whose RMSSE is undefined (series 322 in RN13) and, per test, those with a non-finite value; fixed by the data set; one run, no interim analysis; supported if p_cov < alpha; not supported if low_cov >= 0; verdict computed
  plan: lab plan PL8; planned 2026-11-13T10:26:26Z; anchor git_remote
C20 [descriptive; secondary; support: empirical_quant E5 (E5.R2, E5.T3.r3) artefacts A8; verifiability open; planning confirmatory; outcome supported]
  On [[D18:electricity hourly]] with [[D19:rolling-origin evaluation]], [[D20:smooth TBATS dnorm]] takes less [[D13:elapsed time]] per series than [[D1:smooth TBATS]] with its default distribution: the geometric mean over series of the ratio of their elapsed times is 0.6368 (99% confidence interval 0.619 to 0.6552).
  scope: data_type: 370 hourly electricity series of clients of one Portuguese utility, 2011-2014 | conditions: 7 daily origins in the last week of each series, ending 2014-09-08; 1008-hour fitting windows; horizon 48; periods 24 and 168; comparator: smooth TBATS
  extends B4: De Livera, Hyndman and Snyder introduced TBATS; this claim is about the implementation of smooth, which places the harmonics in ADAM's state space core, compared with two other implementations.
  test: frequentist; alpha 0.01; test one-sided one-sample t-tests over series on the per-series means over the 7 origins: H20, the log ratio of RMSSE, smooth TBATS (auto) over smooth TBATS dnorm, H0: mean >= 0; H21, the coverage of the 95% interval of smooth TBATS dnorm minus 0.95, H0: mean >= 0; H22, the log ratio of the elapsed time, smooth TBATS dnorm over smooth TBATS (auto), H0: mean >= 0. Intervals are 99% t-intervals; relative RMSSE and relative elapsed time (dnorm over auto) are the exponentials of the mean log ratios and their intervals; sides less; correction holm over the three t-tests (H20, H21, H22); sample All 370 series of the electricity data (TM19) less those whose RMSSE is undefined (series 322 in RN13) and, per test, those with a non-finite value; fixed by the data set; one run, no interim analysis; supported if p_time < alpha; not supported if low_time >= 1; verdict computed
  plan: lab plan PL8; planned 2026-11-13T10:26:26Z; anchor git_remote

EVIDENCE
E1 [simulation] The [[D14:formulation checks]] of [[D1:smooth TBATS]], run once with the seeds 101 to 110 (lab run RN6, plan PL1): the largest relative difference of the one-step fitted values from an independent implementation of the recursion of [[D2:De Livera TBATS]] over 360 cases (H1), the largest absolute in-sample error of backcasting on 10 noise-free series (H2), and, over nine pairs of smoothing parameter and AR(1) coefficient, the largest distance of the impulse response of smooth TBATS from that of an additive ARMA component and the smallest from that of ARMA errors (H3). The per-case values are in the CSV of the lab results (A8).
  setup: studied D1, D2; procedure D14
  E1.R1 max relative difference of fitted values over all cases, smooth TBATS vs De Livera recursion (max) = 5.1122857914327425e-14 {seeds: [101, 102, 103, 104, 105, 106, 107, 108, 109, 110], cases: 360}
  E1.R2 max absolute in-sample error over all noise-free series, backcasting (max) = 1.7696635268293903e-09 {seeds: [101, 102, 103, 104, 105, 106, 107, 108, 109, 110], n: 300}
  E1.R3 max absolute difference of smooth's impulse response from alpha + phi^j over all cases (max) = 2.220446049250313e-16
  E1.R4 min over cases of the max absolute difference of smooth's impulse response from the ARMA-errors response (min) = 0.01651176558114527
E2 [quant; data_origin secondary] Benchmark of [[D1:smooth TBATS]] against [[D3:forecast::tbats]], [[D4:AutoTBATS]], [[D5:ADAM ETS]] and [[D6:seasonal naive 168]] on the 414 series of [[D7:M4 hourly]] with [[D9:fixed-origin evaluation]] (the M4 test split, 48 hours ahead), run once under plan PL3 (lab run RN8). Each fit is single-threaded; a failed fit gets the seasonal naive 168 forecasts and no interval. Per series, [[D10:MASE]], the coverage of the 95% interval and the elapsed time (averaged over the origins where there are several); the relative MASE of smooth TBATS to each comparator is the geometric mean over series of the ratio of their MASE, with a 99% t-interval on the log scale; the one-sided t-tests on the mean log ratios are adjusted by Holm over four; the [[D15:Nemenyi test]] ranks the five methods within each series. The sMAPE that the run also computed is in the CSV of the lab results only (decision DC4 of the lab record).
  setup: studied D1, D3, D4, D5, D6; cases D7; procedure D9, D15; lens D10, D11, D12, D13
  E2.R1 D11 (geometric mean) = 0.8317576290033031 99% confidence interval 0.7793039397579915 to 0.8877418913345124 {comparator: D3}
  E2.R2 D11 (geometric mean) = 0.780315891451513 99% confidence interval 0.7242363686872306 to 0.840737798842475 {comparator: D4}
  E2.R3 D11 (geometric mean) = 0.9260655272734568 99% confidence interval 0.824281045050103 to 1.0404186362821646 {comparator: D5}
  E2.R4 D11 (geometric mean) = 0.5067448313602549 99% confidence interval 0.44786668083806935 to 0.5733633134525995 {comparator: D6}
  E2.R5 relative elapsed time (geometric mean) = 0.5790894532352115 99% confidence interval 0.5389759363891272 to 0.6221884358973419 {comparator: D3}
  E2.R6 critical distance, Nemenyi test (MASE) = 0.35767939611022115 {level: 0.99}
  E2.R7 series in Nemenyi test (count) = 414
  E2.R8 p-value, rmcb test of equal mean ranks (MASE) (p_value) = 1.1039717573166142e-32
  E2.T1 Per method: mean and median MASE over series, coverage of the 95% prediction intervals, median elapsed time per series in seconds, series with a failed fit, and the mean rank of MASE in the Nemenyi test with the bounds of its 99% interval.
  | row | method | D10 (mean) | D10 (median) | D12 {nominal level: 0.95} (mean) | D13 (median) | series failed (count) | mean rank of MASE, Nemenyi test (mean) | mean rank of MASE, Nemenyi test {bound: 99% interval, lower} | mean rank of MASE, Nemenyi test {bound: 99% interval, upper} |
  | r1 | D1 | 1.029 | 0.87 | 0.9273349436392914 | 14.18 | 0 | 2.5724637681159437 | 2.394 | 2.751 |
  | r2 | D3 | 1.304 | 0.9941 | 0.9101 | 24.4 | 0 | 2.9541062801932383 | 2.775 | 3.133 |
  | r3 | D4 | 1.516 | 0.9836 | 0.9183 | 21.42 | 0 | 3.07729468599034 | 2.898 | 3.256 |
  | r4 | D5 | 2.11 | 0.7984 | 0.9054 | 1.31 | 0 | 2.618 | 2.44 | 2.797 |
  | r5 | D6 | 2.867 | 1.397 |  | 4.323e-05 | 0 | 3.778 | 3.599 | 3.957 |
  E2.T2 Per comparator: the series the relative MASE of smooth TBATS to it is computed on, and those left out because the MASE of smooth TBATS or of the comparator is zero. {method: D1}
  | row | comparator | series in relative MASE (count) | series excluded by zero MASE (count) |
  | r1 | D3 | 414 | 0 |
  | r2 | D4 | 414 | 0 |
  | r3 | D5 | 414 | 0 |
  | r4 | D6 | 414 | 0 |
  E2.T3 The one-sided t-tests of the plan on the per-series log ratios of smooth TBATS to the comparator: p-value and p-value adjusted by Holm over the four tests.
  | row | comparator | measure | p-value, one-sided t-test (p_value) | Holm-adjusted p-value, one-sided t-test (p_value) |
  | r1 | D3 | MASE | 5.799e-19 | 5.798511501263025e-19 |
  | r2 | D4 | MASE | 1.349e-22 | 2.6978102344588355e-22 |
  | r3 | D6 | MASE | 5.031e-38 | 1.5092330045971394e-37 |
  | r4 | D3 | elapsed time | 1.154e-61 | 4.6151072509330304e-61 |
E3 [quant; data_origin secondary] Benchmark of [[D1:smooth TBATS]] against [[D3:forecast::tbats]], [[D4:AutoTBATS]], [[D5:ADAM ETS]] and [[D6:seasonal naive 168]] on the 414 series of [[D7:M4 hourly]] with [[D9:fixed-origin evaluation]] (the M4 test split, 48 hours ahead), run once under plan PL5 (lab run RN11). Each fit is single-threaded; a failed fit gets the seasonal naive 168 forecasts and no interval. Per series, [[D16:RMSSE]], the coverage of the 95% interval and the elapsed time (averaged over the origins where there are several); the relative RMSSE of smooth TBATS to each comparator is the geometric mean over series of the ratio of their RMSSE, with a 99% t-interval on the log scale; the one-sided t-tests on the mean log ratios are adjusted by Holm over four; the [[D15:Nemenyi test]] ranks the five methods within each series.
  setup: studied D1, D3, D4, D5, D6; cases D7; procedure D9, D15; lens D16, D17, D12, D13
  E3.R1 D17 (geometric mean) = 0.8480372827132892 99% confidence interval 0.7969221555458947 to 0.9024309687802653 {comparator: D3}
  E3.R2 D17 (geometric mean) = 0.7959442609119876 99% confidence interval 0.741071448751255 to 0.854880143535765 {comparator: D4}
  E3.R3 D17 (geometric mean) = 0.9482580389950931 99% confidence interval 0.8470034046237921 to 1.0616171122927285 {comparator: D5}
  E3.R4 D17 (geometric mean) = 0.535834976024436 99% confidence interval 0.47846285660893406 to 0.600086542905422 {comparator: D6}
  E3.R5 relative elapsed time (geometric mean) = 0.568175851157546 99% confidence interval 0.5281131840262834 to 0.6112776722925655 {comparator: D3}
  E3.R6 critical distance, Nemenyi test (RMSSE) = 0.35767939611022115 {level: 0.99}
  E3.R7 series in Nemenyi test (count) = 414
  E3.R8 p-value, rmcb test of equal mean ranks (RMSSE) (p_value) = 4.096753399289539e-34
  E3.T1 Per method: mean and median RMSSE over series, coverage of the 95% prediction intervals, median elapsed time per series in seconds, series with a failed fit, and the mean rank of RMSSE in the Nemenyi test with the bounds of its 99% interval.
  | row | method | D16 (mean) | D16 (median) | D12 {nominal level: 0.95} (mean) | D13 (median) | series failed (count) | mean rank of RMSSE, Nemenyi test (mean) | mean rank of RMSSE, Nemenyi test {bound: 99% interval, lower} | mean rank of RMSSE, Nemenyi test {bound: 99% interval, upper} |
  | r1 | D1 | 0.8294 | 0.6242 | 0.9273 | 12.25 | 0 | 2.562801932367151 | 2.384 | 2.742 |
  | r2 | D3 | 0.9094 | 0.698 | 0.9101 | 21.84 | 0 | 2.9371980676328517 | 2.758 | 3.116 |
  | r3 | D4 | 1.063 | 0.6854 | 0.9183 | 19.7 | 0 | 3.0434782608695667 | 2.865 | 3.222 |
  | r4 | D5 | 2.1 | 0.6314 | 0.9055 | 1.112 | 0 | 2.645 | 2.466 | 2.824 |
  | r5 | D6 | 1.453 | 1.095 |  | 4.024e-05 | 0 | 3.812 | 3.633 | 3.99 |
  E3.T2 Per comparator: the series the relative RMSSE of smooth TBATS to it is computed on, and those left out because the RMSSE of smooth TBATS or of the comparator is zero. {method: D1}
  | row | comparator | series in relative RMSSE (count) | series excluded by zero RMSSE (count) |
  | r1 | D3 | 414 | 0 |
  | r2 | D4 | 414 | 0 |
  | r3 | D5 | 414 | 0 |
  | r4 | D6 | 414 | 0 |
  E3.T3 The one-sided t-tests of the plan on the per-series log ratios of smooth TBATS to the comparator: p-value and p-value adjusted by Holm over the four tests.
  | row | comparator | measure | p-value, one-sided t-test (p_value) | Holm-adjusted p-value, one-sided t-test (p_value) |
  | r1 | D3 | RMSSE | 9.427e-18 | 9.427033177562526e-18 |
  | r2 | D4 | RMSSE | 1.181e-21 | 2.3628603624600894e-21 |
  | r3 | D6 | RMSSE | 4.342e-38 | 1.302649972219819e-37 |
  | r4 | D3 | elapsed time | 4.715e-63 | 1.886e-62 |
E4 [quant; data_origin secondary] Benchmark of [[D1:smooth TBATS]] against [[D3:forecast::tbats]], [[D4:AutoTBATS]], [[D5:ADAM ETS]] and [[D6:seasonal naive 168]] on the 370 series of [[D18:electricity hourly]] with [[D19:rolling-origin evaluation]] (7 daily origins of the last week, 1008-hour fitting windows, 48 hours ahead; series 322, constant in its windows, has an undefined RMSSE and is left out), run once under plan PL7 (lab run RN13). Each fit is single-threaded; a failed fit gets the seasonal naive 168 forecasts and no interval. Per series, [[D16:RMSSE]], the coverage of the 95% interval and the elapsed time (averaged over the origins where there are several); the relative RMSSE of smooth TBATS to each comparator is the geometric mean over series of the ratio of their RMSSE, with a 99% t-interval on the log scale; the one-sided t-tests on the mean log ratios are adjusted by Holm over four; the [[D15:Nemenyi test]] ranks the five methods within each series.
  setup: studied D1, D3, D4, D5, D6; cases D18; procedure D19, D15; lens D16, D17, D12, D13
  E4.R1 D17 (geometric mean) = 0.9752899990850776 99% confidence interval 0.9470396739420402 to 1.0043830353548469 {comparator: D3}
  E4.R2 D17 (geometric mean) = 0.990872986502657 99% confidence interval 0.9753390861558684 to 1.006654290099668 {comparator: D4}
  E4.R3 D17 (geometric mean) = 1.0042706046509193 99% confidence interval 0.7972644036763257 to 1.2650250565750576 {comparator: D5}
  E4.R4 D17 (geometric mean) = 0.8243857583084898 99% confidence interval 0.7980923108751354 to 0.8515454531276542 {comparator: D6}
  E4.R5 relative elapsed time (geometric mean) = 0.6094493108259951 99% confidence interval 0.5799927267313179 to 0.6404019315199876 {comparator: D3}
  E4.R6 critical distance, Nemenyi test (RMSSE) = 0.37886188095533324 {level: 0.99}
  E4.R7 series in Nemenyi test (count) = 369
  E4.R8 p-value, rmcb test of equal mean ranks (RMSSE) (p_value) = 1.5420804210195766e-81
  E4.R9 series excluded by undefined RMSSE (count) = 1
  E4.T1 Per method: mean and median RMSSE over series, coverage of the 95% prediction intervals, median elapsed time per series in seconds, series with a failed fit, and the mean rank of RMSSE in the Nemenyi test with the bounds of its 99% interval.
  | row | method | D16 (mean) | D16 (median) | D12 {nominal level: 0.95} (mean) | D13 (median) | series failed (count) | fits failed (count) | mean rank of RMSSE, Nemenyi test (mean) | mean rank of RMSSE, Nemenyi test {bound: 99% interval, lower} | mean rank of RMSSE, Nemenyi test {bound: 99% interval, upper} |
  | r1 | D1 | 0.7948 | 0.6644 | 0.954 | 12.22 | 0 | 0 | 2.4823848238482347 | 2.293 | 2.672 |
  | r2 | D3 | 0.7985 | 0.6878 | 0.9433 | 20.26 | 0 | 0 | 2.558265582655823 | 2.369 | 2.748 |
  | r3 | D4 | 0.7949 | 0.671 | 0.9372 | 15.07 | 0 | 0 | 2.38753387533875 | 2.198 | 2.577 |
  | r4 | D5 | 0.8795 | 0.7065 | 0.9776 | 1.245 | 0 | 0 | 3.276 | 3.087 | 3.466 |
  | r5 | D6 | 1.003 | 0.8002 |  | 3.08e-05 | 0 | 0 | 4.295 | 4.106 | 4.485 |
  E4.T2 Per comparator: the series the relative RMSSE of smooth TBATS to it is computed on, and those left out because the RMSSE of smooth TBATS or of the comparator is zero. {method: D1}
  | row | comparator | series in relative RMSSE (count) | series excluded by zero RMSSE (count) |
  | r1 | D3 | 369 | 0 |
  | r2 | D4 | 369 | 0 |
  | r3 | D5 | 369 | 0 |
  | r4 | D6 | 368 | 1 |
  E4.T3 The one-sided t-tests of the plan on the per-series log ratios of smooth TBATS to the comparator: p-value and p-value adjusted by Holm over the four tests.
  | row | comparator | measure | p-value, one-sided t-test (p_value) | Holm-adjusted p-value, one-sided t-test (p_value) |
  | r1 | D3 | RMSSE | 0.01407 | 0.02814260346047013 |
  | r2 | D4 | RMSSE | 0.06692 | 0.06691757930915539 |
  | r3 | D6 | RMSSE | 4.861e-42 | 1.4582738129581806e-41 |
  | r4 | D3 | elapsed time | 3.609e-85 | 1.444e-84 |
E5 [quant; data_origin secondary] [[D20:smooth TBATS dnorm]] against [[D1:smooth TBATS]] (distribution "auto") on the 370 series of [[D18:electricity hourly]] with [[D19:rolling-origin evaluation]] (the windows of run RN13), run once under plan PL8 (lab run RN14). Both are fitted to each window one after the other in the same single-threaded worker, so that their elapsed times are measured under the same load; a failed fit gets the seasonal naive 168 forecasts and no interval. Per series, the RMSSE, the coverage of the 95% interval and the elapsed time averaged over the 7 origins; one-sided t-tests over series on the mean log ratio of RMSSE (auto over dnorm), the mean coverage of dnorm minus 0.95 and the mean log ratio of elapsed time (dnorm over auto), adjusted by Holm over the three; the [[D15:Nemenyi test]] on the six methods (A1). Series 322 has an undefined RMSSE and is left out.
  setup: studied D20, D1; cases D18; procedure D19; lens D16, D17, D12, D13
  derived from E4 (reanalysis)
  E5.R1 D17 (geometric mean) = 0.9274901866520837 99% confidence interval 0.782479221333724 to 1.099374939144907 {method: D20, comparator: D1}
  E5.R2 relative elapsed time (geometric mean) = 0.636836353873358 99% confidence interval 0.6189769713949341 to 0.6552110342663261 {method: D20, comparator: D1}
  E5.R3 coverage of smooth TBATS dnorm minus 0.95 (mean) = -0.01679894179894176 99% confidence interval -0.02364168981181017 to -0.00995619378607335
  E5.R4 log ratio of RMSSE, smooth TBATS to smooth TBATS dnorm (mean) = 0.07527306498554022 99% confidence interval -0.09474178115542094 to 0.2452879111265014
  E5.R5 log ratio of elapsed time, smooth TBATS dnorm to smooth TBATS (mean) = -0.4512425577124759 99% confidence interval -0.47968720990568653 to -0.42279790551926527
  E5.R6 critical distance, Nemenyi test (RMSSE) = 0.46329573710090965 {level: 0.99}
  E5.R7 series in Nemenyi test (count) = 369
  E5.R8 p-value, rmcb test of equal mean ranks (RMSSE) (p_value) = 1.0372190587495083e-94
  E5.R9 series excluded by undefined RMSSE (count) = 1
  E5.T1 Per method: mean and median RMSSE over series, coverage of the 95% prediction intervals, median elapsed time per series in seconds, and the series and fits that failed.
  | row | method | D16 (mean) | D16 (median) | D12 {nominal level: 0.95} (mean) | D13 (median) | series failed (count) | fits failed (count) |
  | r1 | D1 | 0.7948 | 0.6644 | 0.954 | 12.64 | 0 | 0 |
  | r2 | D20 | 0.7836 | 0.6554 | 0.9332 | 8.031 | 0 | 0 |
  E5.T2 Nemenyi test on the per-series RMSSE of the six methods: smooth TBATS and smooth TBATS dnorm from this run, the other four from run RN13 on the same windows; mean rank with the bounds of its 99% interval.
  | row | method | mean rank of RMSSE, Nemenyi test (mean) | mean rank of RMSSE, Nemenyi test {bound: 99% interval, lower} | mean rank of RMSSE, Nemenyi test {bound: 99% interval, upper} |
  | r1 | D1 | 3.03 | 2.798 | 3.261 |
  | r2 | D3 | 3.122 | 2.89 | 3.354 |
  | r3 | D4 | 2.921 | 2.69 | 3.153 |
  | r4 | D5 | 3.995 | 3.763 | 4.226 |
  | r5 | D6 | 5.165 | 4.934 | 5.397 |
  | r6 | D20 | 2.767 | 2.535 | 2.999 |
  E5.T3 The three one-sided t-tests of plan PL8 over series: p-value, p-value adjusted by Holm over the three, series in the test and series left out for a non-finite value.
  | row | measure | p-value, one-sided t-test (p_value) | Holm-adjusted p-value, one-sided t-test (p_value) | series in the t-test (count) | series excluded by a non-finite value (count) |
  | r1 | RMSSE | 0.8738 | 0.8738080346463214 | 369 | 0 |
  | r2 | coverage | 3.054e-10 | 6.107568971470071e-10 | 369 | 0 |
  | r3 | elapsed time | 8.144e-140 | 2.4431847468486607e-139 | 369 | 0 |

LIMITATIONS
L1 [analytic_flexibility; affects C4, C5, C6, C9, C10, C11, C12, C13; could_bias_magnitude; mitigation none] The accuracy measure of the M4 hourly tests changed after their results were seen: MASE decided the tests of C4, C5, C6 and C9 (lab run RN8), the guarantor then judged MASE unsuitable and set RMSSE (decision DC4 of the lab record), and C10 to C13 restate those hypotheses on RMSSE and test them on the same M4 test split (run RN11), so they are not independent of C4 to C6 and C9.
L2 [model_specification; affects C4, C5, C6, C7, C10, C11, C12, C14, C15, C16, C18, C19, C20; reduces_precision; mitigation none] The t-tests and their intervals treat the series as independent; the series of one data set share calendar and weather effects, so the intervals may be too narrow.
L3 [sampling; affects C14, C15, C16, C17, C18, C19, C20; could_bias_magnitude; mitigation none] The electricity evaluation covers one week, the 7 daily origins before 2014-09-08, of the clients of one utility; other weeks or seasons of the year may rank the methods differently.
L4 [computational; affects C7, C20; could_bias_magnitude; mitigation none] Elapsed times depend on the machine and on the language: forecast::tbats runs in R and the other methods in Python, the M4 runs ran on a cloud machine and the electricity runs on the guarantor's computer, and each time includes its language's overhead per fit.
L5 [other; affects C1, C2, C3, C10, C11, C12, C13, C14, C15, C16, C17; reduces_precision; mitigation none] The lab record flags plans PL1, PL5 and PL7 with code changed after the plan; between PL1 and its run only m4_hourly.py changed, not the script the run used; between PL5 and its run only electricity_hourly.py was added; between PL7 and its run the change set the null hypothesis of superiority that PL7's design specifies.

ARTEFACTS
A1 [figure, data_plot] Nemenyi test on the per-series RMSSE of the six methods on the electricity data (369 series, level 0.99): mean rank of each method with its 99% interval, from run RN14 (smooth TBATS, smooth TBATS dnorm) and run RN13 (the other four). shows E5.T2.r1, E5.T2.r2, E5.T2.r3, E5.T2.r4, E5.T2.r5, E5.T2.r6
A2 [table] CSV written by run RN14 with the per-method values of smooth TBATS and smooth TBATS dnorm (E5.T1), at full precision.
A3 [table] CSV written by run RN14 with the three t-tests of plan PL8 and the relative RMSSE and elapsed time with their intervals (E5.T3, E5.R1 to E5.R5), at full precision.
A4 [table] CSV written by run RN14 with the Nemenyi test of the six methods: mean ranks, intervals, critical distance (E5.T2, E5.R6 to E5.R8), at full precision.
A5 [data] M4 Hourly-train.csv (text/csv), saved by hand on 2026-11-11; recorded in the lab record as SR1 on 2026-11-11. venue: GitHub, Mcompetitions/M4-methods. Written by others. M4 competition hourly data, train samples, one series per row Published by a third party at the URI; the claimset gives its hash, not the file, and the file keeps its publisher's terms.
A6 [data] M4 Hourly-test.csv (text/csv), saved by hand on 2026-11-11; recorded in the lab record as SR2 on 2026-11-11. venue: GitHub, Mcompetitions/M4-methods. Written by others. M4 competition hourly data, test samples, one series per row Published by a third party at the URI; the claimset gives its hash, not the file, and the file keeps its publisher's terms.
A7 [data] GluonTS electricity_nips data set (application/gzip), saved by hand on 2026-11-12; recorded in the lab record as SR3 on 2026-11-12. venue: GitHub, mbohlkeschneider/gluon-ts (branch mv_release). Written by others. Hourly electricity consumption (kW) of 370 clients of a Portuguese utility, from the UCI ElectricityLoadDiagrams20112014 data, as prepared for DeepAR (Salinas et al.): train/data.json ends 2014-09-01 01:00, test/data.json holds 7 daily rolling windows ending 2014-09-02 to 2014-09-08 01:00, in GluonTS JSON lines. Published by a third party at the URI; the claimset gives its hash, not the file, and the file keeps its publisher's terms.
A8 [data] Every result of the lab record (1308 results of 14 runs) at full precision: the lab result's ID, its run, the quantity as the run's script named it, its conditions and its value (both as JSON). The evidence's tables give the values to four significant digits.
A9 [lab_record] Lab record of the study: questions, hypotheses, plans, runs, results and decisions, as an append-only, hash-chained event log (Claimset lab record specification v0.21, begun 2026-11-11; exported with claimset 0.41.6).
A10 [code] The study's scripts: formulation_checks.py (E1), m4_hourly.py and m4_forecast_tbats.R (E2, E3), electricity_hourly.py (E4) and electricity_dnorm.py (E5), at the last commit of the study's code; each evidence names the commit it ran at.

REFERENCES
B1 https://raw.githubusercontent.com/Mcompetitions/M4-methods/master/Dataset/Train/Hourly-train.csv (url)
B2 https://raw.githubusercontent.com/Mcompetitions/M4-methods/master/Dataset/Test/Hourly-test.csv (url)
B3 https://raw.githubusercontent.com/mbohlkeschneider/gluon-ts/mv_release/datasets/electricity_nips.tar.gz (url)
B4 10.1198/jasa.2011.tm09771 (doi)
B5 10.18637/jss.v027.i03 (doi)
B6 10.1016/j.ijforecast.2019.04.014 (doi)
B7 10.1016/j.ijforecast.2021.11.013 (doi)
B8 10.1201/9781003452652 (doi)
B9 10.24432/C58C86 (doi)
B10 10.1016/j.ijforecast.2006.03.001 (doi)
B11 https://jmlr.org/papers/v7/demsar06a.html (url)
B12 https://github.com/Nixtla/statsforecast (url)

SCORES
Scores are computed by rules from the claimset file (EntryLib rubric 0.4): they check the record, not the science, and may change as the rubric and reviews develop.
Support of the paper: 91 (high), the mean of its 5 principal claims; the lowest is C10 at 89.
C1: Support 94 (high); novelty: new, by the authors
C2: Support 97 (high)
C3: Support 94 (high); novelty: new, by the authors
C4: Support 93 (high); novelty: new, by the authors
C5: Support 93 (high); novelty: new, by the authors
C6: Support 93 (high); novelty: new, by the authors
C7: Support 93 (high); novelty: new, by the authors
C8: Support 100 (high); novelty: new, by the authors
C9: Support 94 (high); novelty: new, by the authors
C10: Support 89 (high); novelty: new, by the authors
C11: Support 92 (high); novelty: new, by the authors
C12: Support 92 (high); novelty: new, by the authors
C13: Support 90 (high); novelty: new, by the authors
C14: Support 92 (high); novelty: new, by the authors
C15: Support 92 (high); novelty: new, by the authors
C16: Support 92 (high); novelty: new, by the authors
C17: Support 90 (high); novelty: new, by the authors
C18: Support 93 (high); novelty: new, by the authors
C19: Support 93 (high); novelty: new, by the authors
C20: Support 90 (high); novelty: new, by the authors
Open problems in the principal claims and what they rest on:
P1 [open; up to -6; C4, C5, C6, C9, C10, C11, C12, C13] Limitation L1 (could bias magnitude, not mitigated): The accuracy measure of the M4 hourly tests changed after their results were seen: MASE decided the tests of C4, C5, C6 and C9 (lab run RN8), the guarantor then judged MASE unsuitable and set RMSSE (decision DC4 of the lab record), and C10 to C13 restate those hypotheses on RMSSE and test them on the same M4 test split (run RN11), so they are not independent of C4 to C6 and C9. To remove it: Mitigate it with evidence, or narrow the claim's scope so that it no longer applies.
P2 [open; up to -6; C14, C15, C16, C17, C18, C19, C20] Limitation L3 (could bias magnitude, not mitigated): The electricity evaluation covers one week, the 7 daily origins before 2014-09-08, of the clients of one utility; other weeks or seasons of the year may rank the methods differently. To remove it: Mitigate it with evidence, or narrow the claim's scope so that it no longer applies.
P3 [plan; up to -3; C1, C3, C10, C13, C17] The lab record flags the test: code changed after plan. To remove it: Rerun the test as planned, or explain the flag in a limitation.
P4 [open; up to -1; C4, C5, C6, C7, C10, C11, C12, C14, C15, C16, C18, C19, C20] Limitation L2 (reduces precision, not mitigated): The t-tests and their intervals treat the series as independent; the series of one data set share calendar and weather effects, so the intervals may be too narrow. To remove it: Mitigate it with evidence, or narrow the claim's scope so that it no longer applies.
P5 [open; up to -3; C1, C2, C3, C10, C11, C12, C13, C14, C15, C16, C17] Limitation L5 (reduces precision, not mitigated): The lab record flags plans PL1, PL5 and PL7 with code changed after the plan; between PL1 and its run only m4_hourly.py changed, not the script the run used; between PL5 and its run only electricity_hourly.py was added; between PL7 and its run the change set the null hypothesis of superiority that PL7's design specifies. To remove it: Mitigate it with evidence, or narrow the claim's scope so that it no longer applies.

HOW TO CITE
This claimset: Svetunkov, I. (guarantor) (2026). TBATS in smooth: its formulation, and its accuracy against forecast::tbats and AutoTBATS on hourly data. EntryLib. entrylib:2026.000007@v1. https://entrylib.org/p/2026.000007@v1
One claim of it: by its identifier, as entrylib:2026.000007@v1#C1 for claim C1. Each principal claim has its own page, as https://entrylib.org/p/2026.000007/C1.