IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0169981.html
   My bibliography  Save this article

Time-Varying Transition Probability Matrix Estimation and Its Application to Brand Share Analysis

Author

Listed:
  • Tomoaki Chiba
  • Hideitsu Hino
  • Shotaro Akaho
  • Noboru Murata

Abstract

In a product market or stock market, different products or stocks compete for the same consumers or purchasers. We propose a method to estimate the time-varying transition matrix of the product share using a multivariate time series of the product share. The method is based on the assumption that each of the observed time series of shares is a stationary distribution of the underlying Markov processes characterized by transition probability matrices. We estimate transition probability matrices for every observation under natural assumptions. We demonstrate, on a real-world dataset of the share of automobiles, that the proposed method can find intrinsic transition of shares. The resulting transition matrices reveal interesting phenomena, for example, the change in flows between TOYOTA group and GM group for the fiscal year where TOYOTA group’s sales beat GM’s sales, which is a reasonable scenario.

Suggested Citation

  • Tomoaki Chiba & Hideitsu Hino & Shotaro Akaho & Noboru Murata, 2017. "Time-Varying Transition Probability Matrix Estimation and Its Application to Brand Share Analysis," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-13, January.
    • Handle: RePEc:plo:pone00:0169981
    DOI: 10.1371/journal.pone.0169981
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0169981
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0169981&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0169981?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
    ---><---

    References listed on IDEAS

    as
    1. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    2. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yuan, Qianshun & Semba, Sherehe & Zhang, Jing & Weng, Tongfeng & Gu, Changgui & Yang, Huijie, 2021. "Multi-scale transition matrix approach to time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).

    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. Wei Tang & Steven L Bressler & Chad M Sylvester & Gordon L Shulman & Maurizio Corbetta, 2012. "Measuring Granger Causality between Cortical Regions from Voxelwise fMRI BOLD Signals with LASSO," PLOS Computational Biology, Public Library of Science, vol. 8(5), pages 1-14, May.
    2. Chia-Yen Lee & Chen-Fu Chien, 2022. "Pitfalls and protocols of data science in manufacturing practice," Journal of Intelligent Manufacturing, Springer, vol. 33(5), pages 1189-1207, June.
    3. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    4. Emeka Nkoro & Aham Kelvin Uko, 2016. "Exchange Rate and Inflation Volatility and Stock Prices Volatility: Evidence from Nigeria, 1986-2012," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 6(6), pages 1-4.
    5. Czujack, Corinna & Flôres Junior, Renato Galvão & Ginsburgh, Victor, 1995. "On long-run price comovements between paintings and prints," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 269, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    6. Sotirios Varelas, 2022. "Virtual Immersive Platforms as a Strategic Innovative Destination Marketing Tool in the COVID-19 Era," Sustainability, MDPI, vol. 14(19), pages 1-15, October.
    7. Loperfido, Nicola, 2010. "A note on marginal and conditional independence," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1695-1699, December.
    8. Hyunsoo Kang, 2022. "Impacts of Income Inequality and Economic Growth on CO 2 Emissions: Comparing the Gini Coefficient and the Top Income Share in OECD Countries," Energies, MDPI, vol. 15(19), pages 1-15, September.
    9. KAMKOUM, Arnaud Cedric, 2023. "The Federal Reserve’s Response to the Global Financial Crisis and its Effects: An Interrupted Time-Series Analysis of the Impact of its Quantitative Easing Programs," Thesis Commons d7pvg, Center for Open Science.
    10. Bierens, H.J. & Broersma, L., 1991. "The relation between unemployment and interest rate : some international evidence," Serie Research Memoranda 0112, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    11. Zamani, Mehrzad, 2007. "Energy consumption and economic activities in Iran," Energy Economics, Elsevier, vol. 29(6), pages 1135-1140, November.
    12. Jumah, Adusei & Kunst, Robert M., 2001. "The Effects of Exchange-Rate Exposures on Equity Asset Markets," Economics Series 94, Institute for Advanced Studies.
    13. Muhammad Shafiullah & Ravinthirakumaran Navaratnam, 2016. "Do Bangladesh and Sri Lanka Enjoy Export-Led Growth? A Comparison of Two Small South Asian Economies," South Asia Economic Journal, Institute of Policy Studies of Sri Lanka, vol. 17(1), pages 114-132, March.
    14. Portes, Richard & Santorum, Anita, 1987. "Money and the consumption goods market in China," Journal of Comparative Economics, Elsevier, vol. 11(3), pages 354-371, September.
    15. Alberto Fuertes & Simón Sosvilla-Rivero, 2019. "“Forecasting emerging market currencies: Are inflation expectations useful?”," IREA Working Papers 201918, University of Barcelona, Research Institute of Applied Economics, revised Oct 2019.
    16. Diana Ricciulli-Marín, 2020. "The Fiscal Cost of Conflict: Evidence from La Violencia in Colombia," Cuadernos de Historia Económica 53, Banco de la Republica de Colombia.
    17. Wesam Salah Alaloul & Muhammad Ali Musarat & Muhammad Babar Ali Rabbani & Qaiser Iqbal & Ahsen Maqsoom & Waqas Farooq, 2021. "Construction Sector Contribution to Economic Stability: Malaysian GDP Distribution," Sustainability, MDPI, vol. 13(9), pages 1-26, April.
    18. Xiaojie Xu, 2017. "The rolling causal structure between the Chinese stock index and futures," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 31(4), pages 491-509, November.
    19. Hany Eldemerdash & Hugh Metcalf & Sara Maioli, 2014. "Twin deficits: new evidence from a developing (oil vs. non-oil) countries’ perspective," Empirical Economics, Springer, vol. 47(3), pages 825-851, November.
    20. Olivier Damette & Stéphane Goutte, 2021. "Weather, Pollution, and Covid-19 Spread: A Time Series and Wavelet Reassessment," Springer Books, in: Fateh Belaïd & Anna Cretì (ed.), Energy Transition, Climate Change, and COVID-19, pages 95-106, Springer.

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0169981. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.