IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v40y2025i3d10.1007_s00180-024-01531-z.html
   My bibliography  Save this article

Positive time series regression models: theoretical and computational aspects

Author

Listed:
  • Taiane Schaedler Prass

    (Universidade Federal do Rio Grande do Sul)

  • Guilherme Pumi

    (Universidade Federal do Rio Grande do Sul)

  • Cleiton Guollo Taufemback

    (Universidade Federal do Rio Grande do Sul)

  • Jonas Hendler Carlos

    (Universidade Federal do Rio Grande do Sul)

Abstract

This paper discusses dynamic ARMA-type regression models for positive time series, which can handle bounded non-Gaussian time series without requiring data transformations. Our proposed model includes a conditional mean modeled by a dynamic structure containing autoregressive and moving average terms, time-varying covariates, unknown parameters, and link functions. Additionally, we present the PTSR package and discuss partial maximum likelihood estimation, asymptotic theory, hypothesis testing inference, diagnostic analysis, and forecasting for a variety of regression-based dynamic models for positive time series. A Monte Carlo simulation and a real data application are provided.

Suggested Citation

  • Taiane Schaedler Prass & Guilherme Pumi & Cleiton Guollo Taufemback & Jonas Hendler Carlos, 2025. "Positive time series regression models: theoretical and computational aspects," Computational Statistics, Springer, vol. 40(3), pages 1185-1215, March.
  • Handle: RePEc:spr:compst:v:40:y:2025:i:3:d:10.1007_s00180-024-01531-z
    DOI: 10.1007/s00180-024-01531-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-024-01531-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00180-024-01531-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Víctor Leiva & Helton Saulo & Rubens Souza & Robert G. Aykroyd & Roberto Vila, 2021. "A new BISARMA time series model for forecasting mortality using weather and particulate matter data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 346-364, March.
    2. Guilherme Pumi & Taiane Schaedler Prass & Rafael Rigão Souza, 2021. "A dynamic model for double‐bounded time series with chaotic‐driven conditional averages," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 68-86, March.
    3. Charles, Amélie & Darné, Olivier & Kim, Jae H., 2011. "Small sample properties of alternative tests for martingale difference hypothesis," Economics Letters, Elsevier, vol. 110(2), pages 151-154, February.
    4. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 134(1), pages 151-185, September.
    5. Vincent Goulet & Christophe Dutang & Mathieu Pigeon, 2008. "actuar : An R Package for Actuarial Science," Post-Print hal-01616144, HAL.
    6. T. Rahul & N. Balakrishnan & N. Balakrishna, 2018. "Time series with Birnbaum‐Saunders marginal distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(4), pages 562-581, July.
    7. Wilfredo Palma & Mauricio Zevallos, 2011. "Fitting non‐Gaussian persistent data," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 27(1), pages 23-36, January.
    8. Leena Kalliovirta, 2012. "Misspecification tests based on quantile residuals," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 358-393, June.
    9. Konstantinos Fokianos & Benjamin Kedem, 2004. "Partial Likelihood Inference For Time Series Following Generalized Linear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 173-197, March.
    10. Kim, Jae H., 2009. "Automatic variance ratio test under conditional heteroskedasticity," Finance Research Letters, Elsevier, vol. 6(3), pages 179-185, September.
    11. Benjamin Kedem & Konstantinos Fokianos, 2002. "Regression Models for Binary Time Series," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 185-199, Springer.
    12. Dutang, Christophe & Goulet, Vincent & Pigeon, Mathieu, 2008. "actuar: An R Package for Actuarial Science," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 25(i07).
    13. Manuel Dominguez & Ignacio Lobato, 2003. "Testing the Martingale Difference Hypothesis," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 351-377.
    14. Fokianos, Konstantinos & Kedem, Benjamin, 1998. "Prediction and Classification of Non-stationary Categorical Time Series," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 277-296, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guilherme Pumi & Taiane Schaedler Prass & Cleiton Guollo Taufemback, 2024. "Unit-Weibull autoregressive moving average models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(1), pages 204-229, March.
    2. João A. Bastos, 2025. "A deep learning test of the martingale difference hypothesis," Working Papers REM 2025/0374, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    3. Karasiński Jacek, 2023. "The adaptive market hypothesis and the return predictability in the cryptocurrency markets," Economics and Business Review, Sciendo, vol. 9(1), pages 94-118, April.
    4. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.
    5. Charles, Amélie & Darné, Olivier & Kim, Jae H., 2011. "Small sample properties of alternative tests for martingale difference hypothesis," Economics Letters, Elsevier, vol. 110(2), pages 151-154, February.
    6. Daeyun Kang & Doojin Ryu & Robert I. Webb, 2025. "Bitcoin as a financial asset: a survey," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 11(1), pages 1-28, December.
    7. Ashok Chanabasangouda Patil & Shailesh Rastogi, 2019. "Time-Varying Price–Volume Relationship and Adaptive Market Efficiency: A Survey of the Empirical Literature," JRFM, MDPI, vol. 12(2), pages 1-18, June.
    8. Lazăr, Dorina & Todea, Alexandru & Filip, Diana, 2012. "Martingale difference hypothesis and financial crisis: Empirical evidence from European emerging foreign exchange markets," Economic Systems, Elsevier, vol. 36(3), pages 338-350.
    9. Charles, Amélie & Darné, Olivier & Kim, Jae H., 2012. "Exchange-rate return predictability and the adaptive markets hypothesis: Evidence from major foreign exchange rates," Journal of International Money and Finance, Elsevier, vol. 31(6), pages 1607-1626.
    10. Köchling, Gerrit & Müller, Janis & Posch, Peter N., 2019. "Does the introduction of futures improve the efficiency of Bitcoin?," Finance Research Letters, Elsevier, vol. 30(C), pages 367-370.
    11. Am鬩e Charles & Olivier Darn頍 & Jae H. Kim & Etienne Redor, 2016. "Stock exchange mergers and market efficiency," Applied Economics, Taylor & Francis Journals, vol. 48(7), pages 576-589, February.
    12. Zdeněk Hlávka & Marie Hušková & Claudia Kirch & Simos G. Meintanis, 2017. "Fourier--type tests involving martingale difference processes," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 468-492, April.
    13. Shimeng Shi & Jia Zhai & Yingying Wu, 2024. "Informational inefficiency on bitcoin futures," The European Journal of Finance, Taylor & Francis Journals, vol. 30(6), pages 642-667, April.
    14. Andrea Flori, 2019. "Cryptocurrencies In Finance: Review And Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-22, August.
    15. Vidal-Tomás, David, 2022. "Which cryptocurrency data sources should scholars use?," International Review of Financial Analysis, Elsevier, vol. 81(C).
    16. Akbar, Muhammad & Ullah, Ihsan & Ali, Shahid & Rehman, Naser, 2024. "Adaptive market hypothesis: A comparison of Islamic and conventional stock indices," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 460-477.
    17. Verheyden, Tim & De Moor, Lieven & Van den Bossche, Filip, 2015. "Towards a new framework on efficient markets," Research in International Business and Finance, Elsevier, vol. 34(C), pages 294-308.
    18. Chu, Jeffrey & Zhang, Yuanyuan & Chan, Stephen, 2019. "The adaptive market hypothesis in the high frequency cryptocurrency market," International Review of Financial Analysis, Elsevier, vol. 64(C), pages 221-231.
    19. Huai-Long Shi & Zhi-Qiang Jiang & Wei-Xing Zhou, 2016. "Time-varying return predictability in the Chinese stock market," Papers 1611.04090, arXiv.org.
    20. Amélie Charles & Olivier Darné & Jae H. Kim & Etienne Redor, 2016. "Stock Exchange Mergers and Market," Post-Print hal-01238707, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:40:y:2025:i:3:d:10.1007_s00180-024-01531-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.