IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v35y2008i7p717-737.html
   My bibliography  Save this article

On the efficiency of regression analysis with AR(p) errors

Author

Listed:
  • Teresa Alpuim
  • Abdel El-Shaarawi

Abstract

In this paper we will consider a linear regression model with the sequence of error terms following an autoregressive stationary process. The statistical properties of the maximum likelihood and least squares estimators of the regression parameters will be summarized. Then, it will be proved that, for some typical cases of the design matrix, both methods produce asymptotically equivalent estimators. These estimators are also asymptotically efficient. Such cases include the most commonly used models to describe trend and seasonality like polynomial trends, dummy variables and trigonometric polynomials. Further, a very convenient asymptotic formula for the covariance matrix will be derived. It will be illustrated through a brief simulation study that, for the simple linear trend model, the result applies even for sample sizes as small as 20.

Suggested Citation

  • Teresa Alpuim & Abdel El-Shaarawi, 2008. "On the efficiency of regression analysis with AR(p) errors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(7), pages 717-737.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:7:p:717-737
    DOI: 10.1080/02664760600679775
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760600679775
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760600679775?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. Dufour, Jean-Marie & Gaudry, Marc J. I. & Liem, Tran Cong, 1980. "The Cochrane-Orcutt procedure numerical examples of multiple admissible minima," Economics Letters, Elsevier, vol. 6(1), pages 43-48.
    2. Sun, Hongguang & Pantula, Sastry G., 1999. "Testing for trends in correlated data," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 87-95, January.
    3. Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
    4. Park, Rolla Edward & Mitchell, Bridger M., 1980. "Estimating the autocorrelated error model with trended data," Journal of Econometrics, Elsevier, vol. 13(2), pages 185-201, June.
    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. Vana-Gür, Laura, 2024. "Multivariate ordinal regression for multiple repeated measurements," Computational Statistics & Data Analysis, Elsevier, vol. 199(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. Chihwa Kao & Jamie Emerson, 1998. "On the Estimation of a Linear Time Trend Regression with a One- Way Error Component Model in the Presence of Serially Correlated Errors," Econometrics 9805004, University Library of Munich, Germany.
    2. Jae Kim & Mahbuba Yeasmin, 2005. "The Size and Power of the Bias-Corrected Bootstrap Test for Regression Models with Autocorrelated Errors," Computational Economics, Springer;Society for Computational Economics, vol. 25(3), pages 255-267, June.
    3. Badi H. Baltagi & Chihwa Kao & Long Liu, 2007. "Asymptotic Properties of Estimators for the Linear Panel Regression Model with Individual Effects and Serially Correlated Errors: The Case of Stationary and Non-Stationary Regressors and Residuals," Center for Policy Research Working Papers 93, Center for Policy Research, Maxwell School, Syracuse University.
    4. Fried, Roland & Gather, Ursula, 2004. "Robust Trend Estimation for AR(1) Disturbances," Technical Reports 2004,64, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. Phillips, Robert F., 2004. "Estimation of a generalized random-effects model: some ECME algorithms and Monte Carlo evidence," Journal of Economic Dynamics and Control, Elsevier, vol. 28(9), pages 1801-1824, July.
    6. Miyazaki, Shigetaka & Griffiths, William E., 1984. "The properties of some covariance matrix estimators in linear models with AR(1) errors," Economics Letters, Elsevier, vol. 14(4), pages 351-356.
    7. Sun, Hongguang & Pantula, Sastry G., 1999. "Testing for trends in correlated data," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 87-95, January.
    8. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2015. "Infant mortality rates: time trends and fractional integration," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 589-602, March.
    9. Conybeare, John A C & Murdoch, James C & Sandler, Todd, 1994. "Alternative Collective-Goods Models of Military Alliances: Theory and Empirics," Economic Inquiry, Western Economic Association International, vol. 32(4), pages 525-542, October.
    10. R S Bivand, 1986. "The Evaluation of Norwegian Regional Policy: Parameter Variation in Regional Shift Models," Environment and Planning C, , vol. 4(1), pages 71-90, March.
    11. Barry T. Hirsch, 1985. "Poverty, Transfers, and Economic Growth," Public Finance Review, , vol. 13(1), pages 81-98, January.
    12. Gospodinov, Nikolay & Otsu, Taisuke, 2012. "Local GMM estimation of time series models with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 170(2), pages 476-490.
    13. Robert Mulligan, 1996. "Export-import endogeneity in the context of the Thirlwall- Hussain model: an application of the Durbin-Wu-Hausman test incorporating a Monte Carlo experiment," Applied Economics Letters, Taylor & Francis Journals, vol. 3(4), pages 275-279.
    14. Anders, Sven M. & Caswell, Julie A., 2006. "Assessing the Impact of Stricter Food Safety Standards on Trade: HACCP in U.S. Seafood Trade with the Developing World," 2006 Annual meeting, July 23-26, Long Beach, CA 21338, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    15. Uri, Noel D., 1995. "Estimating the U.S. demand for sugar in the presence of measurement error in the data," Journal of Policy Modeling, Elsevier, vol. 17(1), pages 59-83, February.
    16. Luis A. Gil-Alana & Tommaso Trani, 2019. "Time Trends and Persistence in the Global CO2 Emissions Across Europe," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 73(1), pages 213-228, May.
    17. Banker, Rajiv D. & Chang, Hsihui & Lee, Seok-Young, 2010. "Differential impact of Korean banking system reforms on bank productivity," Journal of Banking & Finance, Elsevier, vol. 34(7), pages 1450-1460, July.
    18. Georgios Filippou & Athanasios G. Georgiadis & Ashish Kumar Jha, 2024. "Establishing the link: Does web traffic from various marketing channels influence direct traffic source purchases?," Marketing Letters, Springer, vol. 35(1), pages 59-71, March.
    19. James G. MacKinnon, 1978. "On the Role of Jacobian Terms in Maximum Likelihood Estimation," Working Paper 304, Economics Department, Queen's University.
    20. OlaOluwa Simon Yaya & Luis Alberiko Gil-Alana, 2020. "Modelling Long-Range Dependence and Non-linearity in the Infant Mortality Rates of African Countries," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 26(3), pages 303-315, August.

    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:taf:japsta:v:35:y:2008:i:7:p:717-737. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.