IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i24p3890-d1540693.html
   My bibliography  Save this article

A New Random Coefficient Autoregressive Model Driven by an Unobservable State Variable

Author

Listed:
  • Yuxin Pang

    (School of Mathematics, Jilin University, Changchun 130012, China
    These authors contributed equally to this work.)

  • Dehui Wang

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110031, China
    These authors contributed equally to this work.)

Abstract

A novel random coefficient autoregressive model is proposed, and a feature of the model is the non-stationarity of the state equation. The autoregressive coefficient is an unknown function with an unobservable state variable, which can be estimated by the local linear regression method. The iterative algorithm is constructed to estimate the parameters based on the ordinary least squares method. The ordinary least squares residuals are used to estimate the variances of the errors. The Kalman-smoothed estimation method is used to estimate the unobservable state variable because of its ability to deal with non-stationary stochastic processes. These methods allow deriving the analytical solutions. The performance of the estimation methods is evaluated through numerical simulation. The model is validated using actual time series data from the S&P/HKEX Large Cap Index.

Suggested Citation

  • Yuxin Pang & Dehui Wang, 2024. "A New Random Coefficient Autoregressive Model Driven by an Unobservable State Variable," Mathematics, MDPI, vol. 12(24), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3890-:d:1540693
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/24/3890/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/24/3890/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    2. Alexander Aue & Lajos Horváth & Josef Steinebach, 2006. "Estimation in Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 61-76, January.
    3. Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    4. Zhi-Wen Zhao & De-Hui Wang & Cui-Xin Peng & Mei-Li Zhang, 2015. "Empirical Likelihood-based Inference for Stationary-ergodicity of the Generalized Random Coefficient Autoregressive Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(12), pages 2586-2599, June.
    5. Marta Regis & Paulo Serra & Edwin R. van den Heuvel, 2022. "Random autoregressive models: A structured overview," Econometric Reviews, Taylor & Francis Journals, vol. 41(2), pages 207-230, February.
    6. Mikio Ito & Akihiko Noda & Tatsuma Wada, 2014. "International stock market efficiency: a non-Bayesian time-varying model approach," Applied Economics, Taylor & Francis Journals, vol. 46(23), pages 2744-2754, August.
    7. BALESTRA, Pietro, 1970. "On the efficiency of ordinary least-squares in regression models," LIDAM Reprints CORE 71, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Mikio Ito & Akihiko Noda & Tatsuma Wada, 2016. "The evolution of stock market efficiency in the US: a non-Bayesian time-varying model approach," Applied Economics, Taylor & Francis Journals, vol. 48(7), pages 621-635, February.
    9. István Berkes & Lajos Horváth & Shiqing Ling, 2009. "Estimation in nonstationary random coefficient autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 395-416, July.
    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. Chi Yao & Wei Yu & Xuejun Wang, 2023. "Strong Consistency for the Conditional Self-weighted M Estimator of GRCA(p) Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-21, March.
    2. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    3. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2019. "Random coefficient continuous systems: Testing for extreme sample path behavior," Journal of Econometrics, Elsevier, vol. 209(2), pages 208-237.
    4. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    5. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).
    6. Maria Kulikova & Gennady Kulikov, 2023. "Estimation of market efficiency process within time-varying autoregressive models by extended Kalman filtering approach," Papers 2310.04125, arXiv.org.
    7. Zheqi Wang & Dehui Wang & Jianhua Cheng, 2023. "A new autoregressive process driven by explanatory variables and past observations: an application to PM 2.5," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 619-658, June.
    8. Jiang, Jinjin & Li, Haiqi, 2020. "A new measure for market efficiency and its application," Finance Research Letters, Elsevier, vol. 34(C).
    9. Charfeddine, Lanouar & Khediri, Karim Ben & Aye, Goodness C. & Gupta, Rangan, 2018. "Time-varying efficiency of developed and emerging bond markets: Evidence from long-spans of historical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 632-647.
    10. Mikio Ito & Kiyotaka Maeda & Akihiko Noda, 2018. "The futures premium and rice market efficiency in prewar Japan," Economic History Review, Economic History Society, vol. 71(3), pages 909-937, August.
    11. Pınar Evrim Mandacı & F. Dilvin Taskın & Zeliha Can Ergun, 2019. "Adaptive Market Hypothesis," International Journal of Economics & Business Administration (IJEBA), International Journal of Economics & Business Administration (IJEBA), vol. 0(4), pages 84-101.
    12. Abdelhakim Aknouche, 2015. "Quadratic random coefficient autoregression with linear-in-parameters volatility," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 99-125, July.
    13. Mohammed Benmoumen & Imane Salhi, 2023. "The Strong Consistency of Quasi-Maximum Likelihood Estimators for p-order Random Coefficient Autoregressive (RCA) Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 617-632, February.
    14. Deniz Erer & Elif Erer & Selim Güngör, 2023. "The aggregate and sectoral time-varying market efficiency during crisis periods in Turkey: a comparative analysis with COVID-19 outbreak and the global financial crisis," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-25, December.
    15. Askari, Abolfazl & Hajizadeh, Ehsan, 2024. "Exploring market efficiency levels: A powerful approach based on a gamma distribution," Finance Research Letters, Elsevier, vol. 66(C).
    16. Aknouche, Abdelhakim, 2015. "Unified quasi-maximum likelihood estimation theory for stable and unstable Markov bilinear processes," MPRA Paper 69572, University Library of Munich, Germany.
    17. Nielsen, Heino Bohn & Rahbek, Anders, 2014. "Unit root vector autoregression with volatility induced stationarity," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 144-167.
    18. Bercu, Bernard & Blandin, Vassili, 2015. "A Rademacher–Menchov approach for random coefficient bifurcating autoregressive processes," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1218-1243.
    19. Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    20. Khaled Mokni & Ghassen El Montasser & Ahdi Noomen Ajmi & Elie Bouri, 2024. "On the efficiency and its drivers in the cryptocurrency market: the case of Bitcoin and Ethereum," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-25, December.

    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:gam:jmathe:v:12:y:2024:i:24:p:3890-:d:1540693. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.