Pith. sign in

REVIEW 5 major objections 5 minor 300 references

GARTFIMA: a model class that brings tempered fractional dynamics to non-Gaussian time series

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 12:47 UTC pith:LL7DIUEI

load-bearing objection Useful extension of GARFIMA to tempered fractional dynamics, but the printed model definition has an indexing bug and the asymptotics are asserted, not proven. the 5 major comments →

arxiv 2607.19311 v1 pith:LL7DIUEI submitted 2026-07-21 stat.ME

GARTFIMA Models: A Class of Observation-Driven Models with Tempered Fractional Dynamics

Guilherme Pumi , Sharandeep Singh Pandher , Taiane Schaedler Prass This is my paper
classification stat.ME MSC 62M1062M2062F1262G2060G22
keywords time series analysislong-range dependencepartial maximum likelihoodnon-Gaussian time seriesobservation-driven modelstempered fractional differencingsemi-long memoryARTFIMA
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces GARTFIMA, a class of observation-driven models that places a tempered fractional differencing term in the systematic component of a generalized linear model. This lets bounded, positive, or count-valued time series exhibit 'semi-long memory': strong persistence at short lags that decays faster than classical long memory at large lags, while keeping autocovariances summable. The paper derives a partial maximum likelihood estimator with closed-form score and conditional information matrix, reports asymptotic results, and tests the estimator by simulation and on two real datasets (air pollution and squared stock returns). Its central claim is that the estimator is well-behaved in finite samples and that the tempered model represents the dependence structure of real data more faithfully and more parsimoniously than the untempered GARFIMA counterpart.

Core claim

The paper's central claim is that a GARMA-style systematic component η_t = X_t'β + Σ_i φ_i (g(Y_{t−i})−X_{t−i}'β) + Σ_k c_k r_{t−k} — with coefficients c_k from the tempered fractional difference operator (1−e^{-λL})^{-d} — defines a coherent class of observation-driven models for non-Gaussian series with semi-long memory. Because λ > 0 tempers the fractional operator, the model is stationary for any non-integer d and has summable autocovariances, so it retains ARTFIMA's theoretical advantages within a GLM framework that allows bounded, positive, and count outcomes. The authors derive the partial maximum likelihood estimator with closed-form score and conditional information matrix, present

What carries the argument

The carrier of the argument is the tempered fractional difference operator Δ^{d,λ} f(t) = (1−e^{-λL})^d f(t) = Σ_j ω^{d,λ}_j f(t−j) with coefficients ω^{d,λ}_j = (−1)^j C(d,j) e^{-λj}. When placed in the systematic component of a GARMA recursion (4), it defines the GARTFIMA class. The paper's estimation machinery is then built on the infinite-recursion structure: the PMLE score vector and conditional information matrix are expressed in terms of the derivatives of η_t with respect to d and λ, which are obtained by differentiating the coefficients ω^{-d,λ}_j through the digamma function and a link to the ARFIMA expansion coefficients π_k. This gives closed-form recursions that the paper implem

Load-bearing premise

The model's definition relies on the unproven convergence of the infinite recursion in Eq. (4) with the coefficients in Eq. (3), and the coefficient formula as printed has an indexing error that makes the ARTFIMA filter's orientation ambiguous; if the recursion diverges or the equations are misimplemented, the model is not a well-defined process.

What would settle it

Simulate a long sample from the recursion (4)–(3) exactly as printed for a representative pair, say d = 0.7 and λ = 0.1, and compare the sample autocovariance with the theoretical ARTFIMA autocovariance; if the recursion's sample paths diverge or the autocovariance fails to match, the model as defined is not a valid stochastic process, independent of the estimator's finite-sample performance.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Practitioners can fit semi-long memory to data whose natural scale is not Gaussian — counts, proportions, positive measurements — without transforming the data first.
  • Because stationarity does not require d < 0.5 when λ > 0, the estimated d can exceed the classical ARFIMA boundary while still producing a stable, forecastable model.
  • The closed-form score and information matrix make full inference (tests, intervals, residuals, forecasts) available for the class, not just point estimation.
  • The real-data results imply that the tempering parameter can substitute for several high-order ARMA lags, giving a more parsimonious description of persistence.
  • The Monte Carlo results indicate that the estimator is accurate for samples of a few hundred, except in the (1, d, λ, 1) configuration, where weak identifiability produces near-flat likelihood regions and inflated standard errors.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the convergence of the recursion and the coefficient indexing are repaired, the class could serve as a drop-in replacement for Gaussian ARFIMA in fields that currently transform bounded data, such as air-quality monitoring and financial volatility.
  • The parametric-bootstrap ACF comparison used in the paper is portable: it could be adopted as a general diagnostic for any observation-driven model, not just tempered versus untempered ones.
  • The weak-identifiability results suggest that a profile likelihood over λ or a penalized estimator may be needed for the (1, d, λ, 1) specification; the authors identify the problem but leave the remedy open.
  • Since tempering yields summable autocovariances, one might expect PMLE convergence to be faster than in untempered LRD settings — a testable prediction that would extend the paper's finite-sample results.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper introduces GARTFIMA(p,d,λ,q), an observation-driven model in the GARMA family whose systematic component contains a tempered fractional ARTFIMA-type filter. The linear predictor is defined in Eq. (4) using coefficients c_k from Eq. (3). Estimation is by partial maximum likelihood; the authors derive score and conditional information matrix expressions, state large-sample convergence informally, report Monte Carlo medians for two Gamma-ARTFIMA scenarios, and apply the model to daily PM2.5 concentrations and squared AMZN log-returns, comparing against a GARFIMA benchmark. The central claim is that GARTFIMA provides a coherent and practically useful class for non-Gaussian series with semi-long memory.

Significance. If made rigorous, the GARTFIMA class would be a useful bridge between GARMA/GARFIMA and ARTFIMA, with potential applications to positive, bounded, and count data exhibiting tempered persistence. The paper has clear strengths: closed-form score/information expressions are derived, the method is implemented in the BTSR R package, the simulation study covers many configurations, and the empirical sections include parametric-bootstrap ACF comparisons and out-of-sample forecasts. However, the current manuscript does not prove that the defining recursion yields a well-defined stationary process, and the printed coefficient definition is internally inconsistent. These issues are load-bearing for the model definition and for the asymptotic inference claims.

major comments (5)
  1. [§2, Eq. (3) and Eq. (4)] As printed, c_k := Σ_{j=0}^{min{k,q}} θ_j ω^{-d,λ}_{j-k}. For j<k the index j−k is negative, and ω^{d,λ}_j is defined in Eq. (2) only for j≥0. The correct ARTFIMA expansion requires ω^{-d,λ}_{k-j}. The same negative-index inconsistency appears in §3.1: ∂η_t/∂d contains ω^{-d,λ}_{i-k}, while ∂η_t/∂θ_s uses ω^{-d,λ}_{k-s} and ∂η_t/∂λ uses ω^{-d,λ}_{k-i}. A reader implementing the printed equations cannot compute η_t. Please correct the indices and verify that all score equations are mutually consistent.
  2. [§2, Eq. (4)] No parameter space Ω is specified (Ω is used in Eq. (6)), and no conditions are given to ensure that the infinite series in Eq. (4) converges or that the recursion has a unique stationary F_t-adapted solution. The causality/invertibility discussion refers to linear ARTFIMA processes; here r_t = g(Y_t) − g(µ_t) and µ_t depends on η_t, so a separate fixed-point or contraction argument is required. This existence/stationarity result is a premise for the PMLE and for every simulation and application in the paper.
  3. [§3.2, Eq. (8)] The convergence in Eq. (8) and the existence of the limit I(γ) are stated under "some regularity conditions (see the discussion in the next section)", but Section 4 contains no such conditions and no theorem is stated. The paper does not specify the assumptions (compact parameter space, identifiability, stationarity/ergodicity, moment conditions) that justify PMLE consistency, asymptotic normality, and the convergence of the Hessian and information matrix. Since standard errors, p-values, and confidence intervals in Sections 5 and 6 depend on this asymptotic claim, it must be stated precisely and either proved or referenced to a theorem that applies.
  4. [§3.2, Eq. (11)] The chain rule for the conditional information matrix appears to contain an error. From the score in §3.1, ∂ℓ_t/∂µ_t = (1/ν)(Y_t−µ_t)h'(µ_t), so E[∂²ℓ_t/∂µ_t² | F_{t−1}] = −h'(µ_t)/ν. The text instead states −h'(µ_t)/(ν g'(µ_t)) and then sets [E_µ]_{t,t} = h'(µ_t)/(ν g'(µ_t)). With T = diag(1/g'(µ_t)) in Eq. (7), Eq. (11) gives K_ρ,ρ with entries proportional to h'/(ν(g')^3), whereas direct differentiation (or the score outer product) gives h'/(ν(g')^2). Please re-derive Eq. (11).
  5. [§4, Tables 1–2] Tables 1 and 2 report only median estimates over 1000 replications. No standard errors, MSEs, RMSEs, or empirical coverage probabilities are given. The text's conclusions such as "the PMLE performs well" and "estimates improve as n increases" rest on a single summary of central tendency; the reader cannot assess variability, bias-variance trade-off, or the reliability of Wald inference. Please add dispersion measures (e.g., SD or RMSE) and, if standard errors are part of the claim, coverage rates of confidence intervals.
minor comments (5)
  1. [§2, ARTFIMA definition] The displayed definition Φ(L)Y_t = (1−e^{−λ}L)^{−d}Θ(L)ε_t is followed by an integer-d simplification stated in the equivalent form Φ(L)(1−e^{−λ}L)^d Y_t = Θ(L)ε_t. Please reconcile the two conventions in the text so that the integer-d claim follows directly.
  2. [§3.1] The notation "βARFIMA" (paragraph after the score equations) is undefined; it is presumably a typo for GARFIMA or beta-ARFIMA. Please define clearly.
  3. [§3.2, Eq. (7)] In Eq. (7), T is written as diag(1/g'_1(µ_1), ..., 1/g'_1(µ_n)); the subscript in g'_1 should vary with t (or be omitted).
  4. [References] There are several reference problems: "Honsking" should be "Hosking"; Sabzikar et al. (2019a) and (2019b) appear to be the same paper; the Hossain et al. entry has a formatting error in the author list.
  5. [§3.2 and §5/6] The paper advertises hypothesis testing and confidence intervals, but no theorem or method for constructing Wald tests/CIs from the PMLE is stated. If these are obtained from the conditional information matrix, this should be made explicit after the asymptotic results are corrected.

Circularity Check

0 steps flagged

No significant circularity: the PMLE derivation is a direct chain-rule calculation from the model definition, and the empirical claims compare fitted models; unproved convergence and index typos are correctness risks, not circularity.

full rationale

Walking the derivation chain: Eq (4) defines eta_t, Eq (5) defines the conditional log-likelihood, Eq (6) defines the PMLE, and Sections 3.1-3.2 obtain the score and conditional information matrix by differentiating that likelihood. No output in this chain is an input by construction: the d and lambda derivatives are computed from the model equations, not assumed. The Monte Carlo study generates data from the model with fixed true parameters and checks whether the PMLE recovers them; this is an internal consistency check, not a fitted value renamed as a prediction. The applications compare two fitted models on AIC, residual tests, bootstrap ACF bands, and withheld forecasts; the forecasts are genuine out-of-sample evaluations. Self-citations to Pumi et al. (2019) and Pandher et al. (2023) supply the beta/phi/theta recursion derivatives and the BTSR package; these are standard published results and are not the paper's central novel claim, so they are at most a minor self-citation, not load-bearing. The printed negative-index terms in Eq (3) and in some score derivatives, together with the absence of a convergence/stationarity proof for the infinite recursion in Eq (4), are substantive correctness problems in the manuscript's definitions, but a defective or unproved definition is not a circular derivation: the claimed results do not reduce to their inputs. Hence no circular step is established; score 2 reflects only the low-level self-citation reliance.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

The central claim rests on the model definition, the PMLE regularity conditions, and the bootstrap ACF comparison. No additional hidden fitted constants or invented physical entities are introduced; the free-parameter ledger is empty because the model's parameters are what PMLE estimates, not ad hoc tuning constants.

axioms (5)
  • domain assumption Conditional distribution of Y_t|F_{t-1} is in the canonical exponential family with dispersion ν (Eq. 1).
    This restricts the random component but is part of the model definition; the authors note 'GARMA-like' models are possible outside this family.
  • ad hoc to paper The infinite-series recursion in Eq. (4) with c_k from Eq. (3) converges and correctly represents ARTFIMA dynamics for all d, λ.
    No convergence proof is given; Eq. (3) as printed has an index error and the ARTFIMA filter convention is inconsistent, so the model may be ill-defined as written.
  • ad hoc to paper Unstated regularity conditions guarantee PMLE consistency, asymptotic normality, and the convergence in Eq. (8).
    Invoked in Sec. 3.2 but never stated or proved; the claimed hypothesis tests, confidence intervals, and p-values depend on this axiom.
  • domain assumption ARTFIMA integer-d simplifications: d>0 gives ARMA(p+d,q), d<0 gives ARMA(p,q−d).
    These claims are inconsistent with the displayed definition Φ(L)Y_t=(1−e^{−λL})^{-d}Θ(L)ε_t; they hold only under a different convention, creating ambiguity in the model.
  • domain assumption Parametric bootstrap ACF bands (B=10,000) approximate the sampling distribution of the empirical ACF under the fitted model.
    Used in Secs. 5–6 to claim superior fit; the bands ignore parameter estimation uncertainty and the comparison is informal, not a calibrated goodness-of-fit test.

pith-pipeline@v1.3.0-alltime-deepseek · 22135 in / 14820 out tokens · 127562 ms · 2026-08-01T12:47:03.228212+00:00 · methodology

0 comments
read the original abstract

This paper introduces a class of observation-driven models whose systematic component includes a tempered fractional differencing term. This specification generalizes long-range dependent models based on the fractional differencing operator, enabling a more general and robust model specification while offering theoretical advantages. We propose a partial maximum likelihood approach for parameter estimation and address hypothesis testing, confidence intervals, goodness-of-fit assessment, and both in-sample and out-of-sample forecasting. A Monte Carlo simulation study evaluates the finite-sample performance of the proposed estimation method, and an empirical application illustrates the model's practical utility.

Figures

Figures reproduced from arXiv: 2607.19311 by Guilherme Pumi, Sharandeep Singh Pandher, Taiane Schaedler Prass.

Figure 1
Figure 1. Figure 1: Time series plots (top) and ACF and PACF plots (bottom). [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Bootstrap confidence bands for the ACF of (top) Model 1 (Gamma-ARTFIMA) [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Out-of-sample forecast accuracy measure as a function of the horizon for Model 1 [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Out-of-sample forecast accuracy measure as a function of the horizon for Model 1 [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Time series plots (top) and ACF and PACF plots (bottom). [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Bootstrap confidence bands for the ACF of (top) Model 1 (Gamma-ARTFIMA) and [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Out-of-sample forecast accuracy measures as a function of the horizon for Model 1 [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Out-of-sample forecast accuracy measure as a function of the horizon for Model 1 [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

300 extracted references · 23 canonical work pages

  1. [1]

    Helen S. C. Benaduce and Guilherme Pumi , Year =. Journal of Statistical Planning and Inference , Volume=

  2. [2]

    2022 , author =

    Granger causality and time series regression for modeling the migratory dynamics of. 2022 , author =

    2022

  3. [3]

    2016 , author =

    Efficient estimation for time series following generalized linear models , journal =. 2016 , author =

    2016

  4. [4]

    2022 , author =

    Generalized autoregressive moving average models: an efficient estimation approach , journal =. 2022 , author =

    2022

  5. [5]

    Scandinavian Journal of Statistics , volume =

    Pumi, Guilherme and Prass, Taiane Schaedler and Souza, Rafael Rig\ ao , title =. Scandinavian Journal of Statistics , volume =

  6. [6]

    TEST , year =

    Guilherme Pumi and Cristiane Rauber and Fábio Mariano Bayer , title =. TEST , year =

  7. [7]

    Journal of Statistical Planning and Inference , year =

    Guilherme Pumi and Marcio Valk and Cleber Bisognin and Fábio Mariano Bayer and Taiane Schaedler Prass , title =. Journal of Statistical Planning and Inference , year =

  8. [8]

    Davis and William T

    Richard A. Davis and William T. M. Dunsmuir and Sarah B. Streett , journal =. Observation-Driven Models for

  9. [9]

    Poisson Autoregression , journal =

    Konstantinos Fokianos and Anders Rahbek and Dag T. Poisson Autoregression , journal =. 2009 , publisher =

    2009

  10. [10]

    2020 , publisher=

    Roderick Little and Donald Rubin , title=. 2020 , publisher=

    2020

  11. [11]

    2012 , publisher=

    van Bureen, Stef , title=. 2012 , publisher=

    2012

  12. [12]

    Journal of Empirical Finance , volume =

    Modeling corporate defaults:. Journal of Empirical Finance , volume =. 2016 , note =. doi:https://doi.org/10.1016/j.jempfin.2016.02.007 , url =

    work page doi:10.1016/j.jempfin.2016.02.007 2016

  13. [13]

    Journal of Multivariate Analysis , volume =

    Log-linear. Journal of Multivariate Analysis , volume =. 2011 , issn =. doi:https://doi.org/10.1016/j.jmva.2010.11.002 , author =

    doi:10.1016/j.jmva.2010.11.002 2011

  14. [14]

    Journal of Hydrology , Year =

    Kumaraswamy autoregressive moving average models for double bounded environmental data , Author =. Journal of Hydrology , Year =

  15. [15]

    Lopes and Guilherme Pumi and Karine Zaniol , title =

    S\'ilvia R.C. Lopes and Guilherme Pumi and Karine Zaniol , title =. Communications in Statistics - Simulation and Computation , volume =. 2013 , publisher =

    2013

  16. [16]

    Lopes , title =

    Guilherme Pumi and S\'ilvia R.C. Lopes , title =. Journal of Statistical Computation and Simulation , volume =. 2015 , publisher =

    2015

  17. [17]

    2025 , journal=

    Prass, Taiane Schaedler and Pumi, Guilherme and Taufemback, Cleiton Guollo and Carlos, Jonas Hendler , title =. 2025 , journal=

    2025

  18. [18]

    and Bayer, D\'ebora M

    Bayer, F\'abio M. and Bayer, D\'ebora M. and Marinoni, Andrea and Gamba, Paolo , journal=. A Novel. 2020 , volume=

    2020

  19. [19]

    Santos, K. H. and Cribari-Neto, F. , title =. Environmetrics , volume =. 2024 , doi =

    2024

  20. [20]

    2023 , note =

    PPMiss: Copula-Based Estimator for Long-Range Dependent Processes under Missing Data , author =. 2023 , note =

    2023

  21. [21]

    Taiane Schaedler Prass and Guilherme Pumi , year =

  22. [22]

    Statistical Inference for Stochastic Processes , author =

    Memory properties of transformations of linear processes , volume =. Statistical Inference for Stochastic Processes , author =. 2017 , pages =. doi:10.1007/s11203-016-9134-4 , number =

    doi:10.1007/s11203-016-9134-4 2017

  23. [23]

    Taiane Schaedler Prass and Jonas Hendler Carlos and Cleiton Guollo Taufemback , year =

  24. [24]

    and Cribari-Neto, Francisco and Pumi, Guilherme and Bayer, F\'abio M

    Scher, Vin\'icius T. and Cribari-Neto, Francisco and Pumi, Guilherme and Bayer, F\'abio M. , title =. Environmetrics , volume =

  25. [25]

    Bayer, F. M. and Pumi, Guilherme and Pereira, T. L. and Souza, T. C. , title=. Computational And Applied Mathematics , volume=

  26. [26]

    2017 , doi =

    Steffen Moritz and Thomas Bartz-Beielstein , journal =. 2017 , doi =

    2017

  27. [27]

    2021 , doi =

    Journal of Multivariate Analysis , volume =. 2021 , doi =

    2021

  28. [28]

    Statistics and Probability Letters , Year =

    On convergence properties of sums of dependent random variables under second moment and covariance restrictions , Author =. Statistics and Probability Letters , Year =

  29. [29]

    Laws of Chaos , Author =

  30. [30]

    Introduction to the Modern Theory of Dynamical Systems , Author =

  31. [31]

    2009 , edition =

    Markov Chains and Stochastic Stability , author =. 2009 , edition =

    2009

  32. [32]

    2003 , Edition =

    An Introduction to Chaotic Dynamical Systems , Author =. 2003 , Edition =

    2003

  33. [33]

    1998 , Edition =

    Dynamical Systems: Stability, Symbolic Dynamics, and Chaos , Author =. 1998 , Edition =

    1998

  34. [34]

    An Introduction to Ergodic Theory , Author =

  35. [35]

    2025 , note=

    Estimation of Long-Range Dependent Models with Missing Data: to Impute or not to Impute? , author=. 2025 , note=

    2025

  36. [36]

    A three-step approach to production frontier estimation and the

    Danilo Hiroshi Matsuoka and Guilherme Pumi and Hudson da Silva Torrent and Marcio Valk , year=. A three-step approach to production frontier estimation and the. 2311.06086 , archivePrefix=

    arXiv

  37. [37]

    , journal=

    Pe\ na-Ram\'irez, Miguel and Rojas Guerra, Renata and Bayer, F\'abio M. , journal=. The. 2024 , volume=

    2024

  38. [38]

    A long range dependent quantile regression model for time series based on the

    Guilherme Pumi , year=. A long range dependent quantile regression model for time series based on the

  39. [39]

    Applied Mathematical Modelling , volume =

    Camara, Ana Julia Alves and Reisen, Valderio Anselmo and Bondon, Pascal , title =. Applied Mathematical Modelling , volume =. 2025 , doi =

    2025

  40. [40]

    Journal of Time Series Analysis , volume =

    Melo, Moizes and Alencar, Airlane , title =. Journal of Time Series Analysis , volume =. doi:https://doi.org/10.1111/jtsa.12550 , year =

    work page doi:10.1111/jtsa.12550

  41. [41]

    Pandher, S. S. and Hossain, S.and Budsaba K. and Volodin, A. , title =. Communications in Statistics - Theory and Methods , volume =. doi:https://doi.org/10.1080/03610926.2022.2064503 , year =

    arXiv 2022

  42. [42]

    Forecasting the proportion of stored energy using the unit Burr XII quantile autoregressive moving average model , journal =

    Ribeiro, Tatiane Fontana and Pe\ na-Ram\'. Forecasting the proportion of stored energy using the unit Burr XII quantile autoregressive moving average model , journal =. 2023 , volume =. doi:10.1007/s40314-023-02513-5 , url =

    work page doi:10.1007/s40314-023-02513-5 2023

  43. [43]

    Bourguignon, Marcelo and de Medeiros, Rodrigo M. R. , title =. TEST , year =. doi:10.1007/s11749-022-00801-6 , url =

    work page doi:10.1007/s11749-022-00801-6

  44. [44]

    doi:10.22533/at.ed.390241804 , note =

    Aplicações de machine learning: resultados de um curso de verão , author =. doi:10.22533/at.ed.390241804 , note =

    work page doi:10.22533/at.ed.390241804

  45. [45]

    Lopes , title =

    Guilherme Pumi and S\'ilvia R.C. Lopes , title =. Communications in Statistics - Theory and Methods , volume =. 2017 , publisher =

    2017

  46. [46]

    Sílvia R. C. Lopes and Guilherme Pumi , journal =. Copulas related to

  47. [47]

    Tadikamalla , journal =

    Pandu R. Tadikamalla , journal =. A Look at the

  48. [48]

    S\ ao Paulo Journal of Mathematical Sciences , author=

    Copulas, Chaotic Processes and Time Series: a Survey , volume=. S\ ao Paulo Journal of Mathematical Sciences , author=. 2014 , pages=. doi:10.11606/issn.2316-9028.v8i2p241-264 , number=

    work page doi:10.11606/issn.2316-9028.v8i2p241-264 2014

  49. [49]

    Statistical Papers , year=

    A novel copula-based approach for parametric estimation of univariate time series through its covariance decay , author=. Statistical Papers , year=

  50. [50]

    Information flow in the

    Susanne Knoll and Antonio Domingos Padula and Mariane Crespolini dos Santos and Guilherme Pumi and Shudong Zhou and Funing Zhongand and Júlio Otávio Jardim Barcellos , journal=. Information flow in the

  51. [51]

    Journal of Commodity Markets , author=

    The Impact of Chinese imports of soybean on port infrastructure in. Journal of Commodity Markets , author=. 2017 , pages=

    2017

  52. [52]

    Journal of Agribusiness in Developing and Emerging Economies , author=

    The role of distance on international commerce: the impact on. Journal of Agribusiness in Developing and Emerging Economies , author=

  53. [53]

    Land Use Policy , volume=

    The quinoa boom in. Land Use Policy , volume=. 2018 , author=

    2018

  54. [54]

    Bedoya-Perales and Antonio Domingos Padula and Guilherme Pumi , pages=

    Noelia S. Bedoya-Perales and Antonio Domingos Padula and Guilherme Pumi , pages=. Quinoa Expansion in. 2018 , journal=

    2018

  55. [55]

    2023 , journal=

    Assessment of the variation of heavy metals and pesticide residues in native and modern potato (. 2023 , journal=

    2023

  56. [56]

    Bedoya-Perales and Elias Escobedo-Pacheco and Diogo Maus and Alisson Neimaier and Guilherme Pumi , journal=

    Noelia S. Bedoya-Perales and Elias Escobedo-Pacheco and Diogo Maus and Alisson Neimaier and Guilherme Pumi , journal=. Dataset of metals and metalloids in food crops and soils sampled across the mining region of

  57. [57]

    2021 , issn =

    Increasing power plant efficiency with clustering methods and Variable Importance Index assessment , journal =. 2021 , issn =. doi:https://doi.org/10.1016/j.egyai.2021.100084 , author =

    arXiv 2021

  58. [58]

    Environmental Nanotechnology, Monitoring & Management , volume =

    Patterns of accumulation and baseline values for metals in agricultural soils from a copper mining region in southern. Environmental Nanotechnology, Monitoring & Management , volume =. 2023 , issn =. doi:https://doi.org/10.1016/j.enmm.2023.100896 , url =

    arXiv 2023

  59. [59]

    Fernando H. P. S. Mendes and Douglas Eduardo Turatti and Guilherme Pumi , year=. Mitigating the choice of the duration in

  60. [60]

    Guilherme Pumi and Taiane Schaedler Prass and Cleiton Guollo Taufemback , year=

  61. [61]

    Axioms , volume =

    Beta autoregressive moving average model with the. Axioms , volume =. 2024 , author=

    2024

  62. [62]

    and Bayer, F

    Santos, A. and Bayer, F. M. and Canterle, D. R. and Pumi, G. , note=. Kumaraswamy autoregressive moving average model with parametric link functions , year=

  63. [63]

    Beta autoregressive moving average model with varying dispersion , author=

  64. [64]

    Pumi and M

    G. Pumi and M. S. Vieira , note=. Adequacy and performance of some dynamic models for double bounded time series under misspecification , year=

  65. [65]

    Guilherme Pumi and Taiane Schaedler Prass and Marcio Valk and Cleber Bisognin and Fábio Mariano Bayer , title =

  66. [66]

    Katerine Zuniga Lastra and Guilherme Pumi and Taiane Schaedler Prass , title=

  67. [67]

    Brazilian Journal of Probability and Statistics , number =

    Oscar Bustos and Silvia Ojeda and Ronny Vallejos , title =. Brazilian Journal of Probability and Statistics , number =. 2009 , doi =

    2009

  68. [68]

    Nijim and Samuel D

    Yousef W. Nijim and Samuel D. Stearns and Wasfy B. Mikhael , abstract =. Linear. Digital Signal Processing , volume =. 1997 , issn =. doi:https://doi.org/10.1006/dspr.1997.0285 , url =

    arXiv 1997

  69. [69]

    2004 , note =

    A statistical framework for picture reconstruction using 2D AR models , journal =. 2004 , note =. doi:https://doi.org/10.1016/j.imavis.2003.07.010 , author =

    work page doi:10.1016/j.imavis.2003.07.010 2004

  70. [70]

    2022 , issn =

    Computational Statistics & Data Analysis , volume =. 2022 , issn =. doi:https://doi.org/10.1016/j.csda.2022.107453 , author =

    arXiv 2022

  71. [71]

    1997 , publisher=

    Multivariate Models and Multivariate Dependence Concepts , author=. 1997 , publisher=

    1997

  72. [72]

    2013 , publisher=

    An Introduction to Copulas , author=. 2013 , publisher=

    2013

  73. [73]

    2017 , issn =

    Adaptive cost dynamic time warping distance in time series analysis for classification , journal =. 2017 , issn =. doi:https://doi.org/10.1016/j.cam.2017.01.004 , author =

    work page doi:10.1016/j.cam.2017.01.004 2017

  74. [74]

    Abensur, T. C. and Cribari-Neto, F. and Menezes, T. A. , Booktitle =. Impactos Do Programa Bolsa Fam\'ilia Nos Resultados Das Elei

  75. [75]

    IEEE Transactions on Automatic Control , Year =

    A new look at the statistical model identification , Author =. IEEE Transactions on Automatic Control , Year =

  76. [76]

    Akkaya and Moti L

    Ayşen D. Akkaya and Moti L. Tiku , Journal =. Time series. 2005 , Number =

    2005

  77. [77]

    , Author =

    On the Comparison of parametric and nonparametric bootstrap. , Author =. Department of Mathematics Uppsala University , Year =

  78. [78]

    Journal of the Royal Statistical Society

    Asymptotic Properties of Conditional Maximum-Likelihood Estimators , Author =. Journal of the Royal Statistical Society. Series B (Methodological) , Year =

  79. [79]

    The Annals of Mathematical Statistics , Year =

    Distribution of the Serial Correlation Coefficient , Author =. The Annals of Mathematical Statistics , Year =. doi:10.1214/aoms/1177731638 , Publisher =

    arXiv

  80. [80]

    Journal of Econometrics , Year =

    Finite sample properties of estimators for autorregressive moving average models , Author =. Journal of Econometrics , Year =

Showing first 80 references.