IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i17p2997-2999.html
   My bibliography  Save this article

Is a subspace containing a splitting subspace a splitting subspace?

Author

Listed:
  • Triacca, Umberto

Abstract

If V, A and B are three closed subspaces of we say that V is a splitting subspace for A,B if and only if A and B are conditionally orthogonal given V. If V is a splitting subspace for A,B, we shall say that V splits A,B. Rozanov [Rozanov, Y.A., 1979. Stochastic Markovian Fields. In: Developments in Statistics, vol. 2. Academic Press, New York, p. 205] observes that A[perpendicular]BV does not imply that the closed subspace W[superset of or equal to]V splits A,B. However, no example is provided. In this note we provide one.

Suggested Citation

  • Triacca, Umberto, 2008. "Is a subspace containing a splitting subspace a splitting subspace?," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2997-2999, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:2997-2999
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00257-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Khon, R., 1981. "A characterization of Granger-Sims exogeneity," Economics Letters, Elsevier, vol. 8(2), pages 129-133.
    2. Granger, C. W. J., 1980. "Testing for causality : A personal viewpoint," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 329-352, May.
    3. 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.
    4. Lutkepohl, Helmut, 1982. "Non-causality due to omitted variables," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 367-378, August.
    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. John D. Levendis, 2018. "Time Series Econometrics," Springer Texts in Business and Economics, Springer, number 978-3-319-98282-3, April.
    2. Abdur Chowdhury, 1988. "Expenditures and receipts in state and local government finances: Comment," Public Choice, Springer, vol. 59(3), pages 277-285, December.
    3. Erdal Atukeren, 2008. "Christmas cards, Easter bunnies, and Granger-causality," Quality & Quantity: International Journal of Methodology, Springer, vol. 42(6), pages 835-844, December.
    4. Breitung, Jörg & Swanson, Norman Rasmus, 1998. "Temporal aggregation and causality in multiple time series models," SFB 373 Discussion Papers 1998,27, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Darrat, Ali F. & Mukherjee, Tarun K., 1995. "Inter-industry differences and the impact of operating and financial leverages on equity risk," Review of Financial Economics, Elsevier, vol. 4(2), pages 141-155.
    6. Salamaliki, Paraskevi K. & Venetis, Ioannis A., 2013. "Energy consumption and real GDP in G-7: Multi-horizon causality testing in the presence of capital stock," Energy Economics, Elsevier, vol. 39(C), pages 108-121.
    7. Loperfido, Nicola, 2010. "A note on marginal and conditional independence," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1695-1699, December.
    8. Fali Huang & Myoung-Jae Lee, 2010. "Dynamic treatment effect analysis of TV effects on child cognitive development," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(3), pages 392-419.
    9. Bentour, El Mostafa, 2013. "Oil Prices, Drought Periods and Growth Forecasts in Morocco," MPRA Paper 52892, University Library of Munich, Germany.
    10. Cathy W. S. Chen & Sangyeol Lee, 2017. "Bayesian causality test for integer-valued time series models with applications to climate and crime data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 797-814, August.
    11. Jose Perez-Montiel & Carles Manera Erbina, 2019. "Investment Sustained by Consumption: A Linear and Nonlinear Time Series Analysis," Sustainability, MDPI, vol. 11(16), pages 1-15, August.
    12. Ruixiaoxiao Zhang & Geoffrey QP Shen & Meng Ni & Johnny Wong, 2020. "The relationship between energy consumption and gross domestic product in Hong Kong (1992–2015): Evidence from sectoral analysis and implications on future energy policy," Energy & Environment, , vol. 31(2), pages 215-236, March.
    13. Corradi, Valentina & Swanson, Norman R., 2004. "Some recent developments in predictive accuracy testing with nested models and (generic) nonlinear alternatives," International Journal of Forecasting, Elsevier, vol. 20(2), pages 185-199.
    14. Tomaso Aste, 2019. "Cryptocurrency market structure: connecting emotions and economics," Digital Finance, Springer, vol. 1(1), pages 5-21, November.
    15. Zapata, Hector O. & Gil, Jose M., 1999. "Cointegration and causality in international agricultural economics research," Agricultural Economics, Blackwell, vol. 20(1), pages 1-9, January.
    16. Claude Diebolt & Cédric Doliger, 2005. "Becker vs. Easterlin. Education, Fertility and Growth in France after World War II," Working Papers 05-03, Association Française de Cliométrie (AFC).
    17. Bertrand Candelon & Sessi Tokpavi, 2016. "A Nonparametric Test for Granger Causality in Distribution With Application to Financial Contagion," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 240-253, April.
    18. Robert A. Weigand, 1996. "Trading volume and firm size: A test of the information spillover hypothesis," Review of Financial Economics, John Wiley & Sons, vol. 5(1), pages 47-58, December.
    19. Gao, Wei & Cui, Wanqi & Ye, Wenna, 2017. "Directed information graphs for the Granger causality of multivariate time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 701-710.
    20. Tomaso Aste, 2019. "Cryptocurrency market structure: connecting emotions and economics," Papers 1903.00472, arXiv.org.

    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:eee:stapro:v:78:y:2008:i:17:p:2997-2999. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.