IDEAS home Printed from https://ideas.repec.org/p/nbr/nberte/0014.html
   My bibliography  Save this paper

Asymptotic Properties of Quasi-Maximum Likelihood Estimators and Test Statistics

Author

Listed:
  • Thomas E. MaCurdy

Abstract

We examine the implications of arbitrage in a market with many assets. The absence of arbitrage opportunities implies that the linear functionals that give the mean and cost of a portfolio are continuous; hence there exist unique portfolios that represent these functionals. The mean variance efficient set is a cone generated by these portfolios. Ross [16, 18J showed that if there is a factor structure, then the distance between the vector or mean returns and the space spanned by the factor loadings is bounded as the number of assets increases. We show that if the covariance matrix of asset returns has only K unbounded eigenvalues, then the corresponding K eigenvectors converge and play the role of factor loadings in Ross' result. Hence only a principal components analysis is needed to test the arbitrage pricing theory. Our eigenvalue conditional can hold even though conventional measures of the approximation error in a K factor model are unbounded. We also resolve the question of when a market with many assets permits so much diversification that risk-free investment opportunities are available.

Suggested Citation

  • Thomas E. MaCurdy, 1981. "Asymptotic Properties of Quasi-Maximum Likelihood Estimators and Test Statistics," NBER Technical Working Papers 0014, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0014
    Note: LS
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/t0014.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. White, Halbert, 1980. "Nonlinear Regression on Cross-Section Data," Econometrica, Econometric Society, vol. 48(3), pages 721-746, April.
    2. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    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. Emma Tominey, 2010. "The Timing of Parental Income and Child Outcomes: The Role of Permanent and Transitory Shocks," CEE Discussion Papers 0120, Centre for the Economics of Education, LSE.
    2. Jongmoo Jay Choi & Elyas Elyasiani, 1996. "Derivative Exposure and the Interest Rate and Exchange Rate Risks of U.S. Banks," Center for Financial Institutions Working Papers 96-53, Wharton School Center for Financial Institutions, University of Pennsylvania.
    3. Hugo Kruiniger, 2002. "On the Estimation of Panel Regression Models with Fixed Effects," Working Papers 450, Queen Mary University of London, School of Economics and Finance.
    4. Jongmoo Choi & Elyas Elyasiani, 1997. "Derivative Exposure and the Interest Rate and Exchange Rate Risks of U.S. Banks," Journal of Financial Services Research, Springer;Western Finance Association, vol. 12(2), pages 267-286, October.
    5. Hall, Bronwyn H, 1987. "The Relationship between Firm Size and Firm Growth in the U.S. Manufacturing Sector," Journal of Industrial Economics, Wiley Blackwell, vol. 35(4), pages 583-606, June.
    6. Songhua Tan & Qianqian Zhu, 2022. "Asymmetric linear double autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 371-388, May.
    7. Zvi Griliches & Bronwyn H. Hall & Ariel Pakes, 1988. "R&D, Patents, and Market Value Revisited: Is There Evidence of A SecondTechnological Opportunity Related Factor?," NBER Working Papers 2624, National Bureau of Economic Research, Inc.
    8. Choi, Jongmoo Jay & Jiang, Cao, 2009. "Does multinationality matter? Implications of operational hedging for the exchange risk exposure," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 1973-1982, November.
    9. Emma Tominey, 2010. "The Timing of Parental Income and Child Outcomes: The Role of Permanent and Transitory Shocks," Discussion Papers 10/21, Department of Economics, University of York.

    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. Müller, Christine H. & Huggins, Richard & Hwang, Wen-Han, 2011. "Consistent estimation of species abundance from a presence-absence map," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1449-1457, September.
    2. Henry Brady, 1989. "Factor and ideal point analysis for interpersonally incomparable data," Psychometrika, Springer;The Psychometric Society, vol. 54(2), pages 181-202, June.
    3. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
    4. Stoker, Thomas M., 1983. "Aggregation, efficiency and cross section regression," Working papers 1453-83., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    5. Dedi Rosadi & Shelton Peiris, 2014. "Second-order least-squares estimation for regression models with autocorrelated errors," Computational Statistics, Springer, vol. 29(5), pages 931-943, October.
    6. Meitz, Mika & Saikkonen, Pentti, 2011. "Parameter Estimation In Nonlinear Ar–Garch Models," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1236-1278, December.
    7. Ezequiel Uriel Jiménez & María Consuelo Colom & María Cruz Molés & María Luisa Moltó Carbonell, 1998. "- Least Squares Estimates Symetrically Adjusted With No Loss Of Information In The Truncated Tobit Model," Working Papers. Serie EC 1998-25, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    8. Sofie Balcaen & Sophie Manigart & Hubert Ooghe, 2011. "From distress to exit: determinants of the time to exit," Journal of Evolutionary Economics, Springer, vol. 21(3), pages 407-446, August.
    9. Klos, Alexander & Rottke, Simon, 2013. "Saving and Consumption When Children Move Out," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79786, Verein für Socialpolitik / German Economic Association.
    10. Santos-Pérez, Rubén., 2015. "Estimación de la demanda de uso de autos particulares en la zona metropolitana del valle de México: un análisis Tobit," Panorama Económico, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 0(21), pages 85-120, segundo s.
    11. Golob, Thomas F., 1988. "Structural Equation Modeling of Travel Choice Dynamics," University of California Transportation Center, Working Papers qt2kj325qv, University of California Transportation Center.
    12. Börner, Lars & Severgnini, Battista, 2011. "Epidemic trade," Discussion Papers 2011/12, Free University Berlin, School of Business & Economics.
    13. Sengupta Anirban & Wiggins Steven N., 2012. "Comparing Price Dispersion on and off the Internet Using Airline Transaction Data," Review of Network Economics, De Gruyter, vol. 11(1), pages 1-38, March.
    14. Cox, Thomas L. & Briggs, Hugh, 1989. "Heteroscedastic Tobit Models: The Household Demand for Fresh Potatoes Revisited," Staff Papers 200482, University of Wisconsin-Madison, Department of Agricultural and Applied Economics.
    15. Callaway, Brantly & Li, Tong & Oka, Tatsushi, 2018. "Quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods," Journal of Econometrics, Elsevier, vol. 206(2), pages 395-413.
    16. Linnemann, Hans & Verbruggen, Harmen, 1991. "GSTP tariff reduction and its effects on south-south trade in manufactures," World Development, Elsevier, vol. 19(5), pages 539-551, May.
    17. Golob, Thomas F. & Van Wissen, Leo, 1989. "A Joint Household Travel Distance Generation And Car Ownership Model," University of California Transportation Center, Working Papers qt72h4k912, University of California Transportation Center.
    18. K. -L. Wang & Y. -T. Tseng & C. -C. Weng, 2003. "A study of production efficiencies of integrated securities firms in Taiwan," Applied Financial Economics, Taylor & Francis Journals, vol. 13(3), pages 159-167.
    19. Bai, Junfei & Wahl, Thomas I. & McCluskey, Jill J., 2008. "Fluid milk consumption in urban Qingdao, China," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 52(2), pages 1-15.
    20. Lilun Du & Qing Li, 2020. "A Data-Driven Approach to High-Volume Recruitment: Application to Student Admission," Manufacturing & Service Operations Management, INFORMS, vol. 22(5), pages 942-957, September.

    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:nbr:nberte:0014. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    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.