IDEAS home Printed from https://ideas.repec.org/p/ags/queddp/275148.html
   My bibliography  Save this paper

Exact Maximum Likelihood Estimation of Regression Equations with a General Stationary Auto-Regressive Disturbance

Author

Listed:
  • Beach, Charles M.
  • Yeo, Stephen

Abstract

This paper develops an exact maximum likelihood technique for estimating regression equations with general p'th-order autoregressive disturbances. The approach appears to be computationally practical and straightforward, insures the estimated error coefficients satisfy a priori stationarity conditions, and insures convergence of the estimation procedure. Recent expression of the analytic inverse of the covariance matrix of a stationary AR(p) process provides the basis for the iterative algorithms, which employ a modified Gauss-Newton technique utilizing exact first and approximate second derivatives. The relationship between stationarity and the form of the objective function is examined. Empirical estimates are then presented for regression models with and without a lagged dependent variable.

Suggested Citation

  • Beach, Charles M. & Yeo, Stephen, 1979. "Exact Maximum Likelihood Estimation of Regression Equations with a General Stationary Auto-Regressive Disturbance," Queen's Institute for Economic Research Discussion Papers 275148, Queen's University - Department of Economics.
    • Handle: RePEc:ags:queddp:275148
    DOI: 10.22004/ag.econ.275148
    as

    Download full text from publisher

    File URL: https://ageconsearch.umn.edu/record/275148/files/QUEENS-IER-PAPER-343.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.22004/ag.econ.275148?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. Hendry, David F & Mizon, Grayham E, 1978. "Serial Correlation as a Convenient Simplification, not a Nuisance: A Comment on a Study of the Demand for Money by the Bank of England," Economic Journal, Royal Economic Society, vol. 88(351), pages 549-563, September.
    2. Hendry, D F, 1971. "Maximum Likelihood Estimation of Systems of Simultaneous Regression Equations with Errors Generated by a Vector Autoregressive Process," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 12(2), pages 257-272, June.
    3. Oberhofer, W & Kmenta, J, 1974. "A General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models," Econometrica, Econometric Society, vol. 42(3), pages 579-590, May.
    4. M. H. Pesaran, 1973. "Exact Maximum Likelihood Estimation of a Regression Equation with a First-Order Moving-Average Error," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(4), pages 529-535.
    5. D. F. Hendry & P. K. Trivedi, 1972. "Maximum Likelihood Estimation of Difference Equations with Moving Average Errors: A Simulation Study," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 39(2), pages 117-145.
    6. Godfrey, Leslie G, 1978. "Testing for Higher Order Serial Correlation in Regression Equations When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1303-1310, November.
    7. Pagan, Adrian, 1974. "A Generalised Approach to the Treatment of Autocorrelation," Australian Economic Papers, Wiley Blackwell, vol. 13(23), pages 267-280, December.
    8. Kevin Clinton, 1973. "The Demand for Money in Canada, 1955-70: Some Single-Equation Estimates and Stability Tests," Canadian Journal of Economics, Canadian Economics Association, vol. 6(1), pages 53-61, February.
    9. Wayne A. Fuller & James E. Martin, 1961. "The Effects of Autocorrelated Errors on the Statistical Estimation of Distributed Lag Models," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 43(1), pages 71-82.
    10. Sawa, Takamitsu, 1978. "The exact moments of the least squares estimator for the autoregressive model," Journal of Econometrics, Elsevier, vol. 8(2), pages 159-172, October.
    11. 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.
    12. Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665, National Bureau of Economic Research, Inc.
    13. Dent, Warren & Min, An-Sik, 1978. "A Monte Carlo study of autoregressive integrated moving average processes," Journal of Econometrics, Elsevier, vol. 7(1), pages 23-55, February.
    14. Newbold, P & Davies, N, 1978. "Error Mis-Specification and Spurious Regressions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(2), pages 513-519, June.
    15. Anderson, T. W. & Mentz, Raúl P., 1977. "The generalized variance of a stationary autoregressive process," Journal of Multivariate Analysis, Elsevier, vol. 7(4), pages 584-588, December.
    16. Folsom, Roger Nils & Boger, Dan C & Mullikin, Harry C, 1976. "Stability Conditions for Linear Constant Coefficient Difference Equations in Generalized Differenced Form," Econometrica, Econometric Society, vol. 44(3), pages 575-591, May.
    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. Denise R. Osborn, 1976. "Maximum Likelihood Estimation of Moving Average Processes," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 1, pages 75-87, National Bureau of Economic Research, Inc.
    2. Joseph G. Nellis & J. Andrew Longbottom, 1981. "An Empirical Analysis of the Determination of House Prices in the United Kingdom," Urban Studies, Urban Studies Journal Limited, vol. 18(1), pages 9-21, February.
    3. D. J. Carland & A. R. Pagan, 1979. "A Short‐Run Econometric Model of the Japanese Wool Textile Industry," The Economic Record, The Economic Society of Australia, vol. 55(4), pages 317-327, December.
    4. Calzolari, Giorgio, 1987. "La varianza delle previsioni nei modelli econometrici [Forecast variance in econometric models]," MPRA Paper 23866, University Library of Munich, Germany.
    5. van den Berg, G., 1986. "Small-sample properties of estimators of the autocorrelation coefficient," Other publications TiSEM 03414dd6-10fa-4f48-a742-e, Tilburg University, School of Economics and Management.
    6. Mahmood, Talat, 1990. "Die Dynamik der Rentabilität als stochastischer Prozess: eine empirische Zeitreihenanalyse von ausgewählten deutschen und amerikanischen Unternehmen. Vom Fachbereich 20 Informatik der Technischen Univ," EconStor Books, ZBW - Leibniz Information Centre for Economics, number 112236, August.
    7. Gunnar Bårdsen & Eilev S. Jansen & Ragnar Nymoen, 2002. "The Empirical (ir)Relevance of the New Keynesian Phillips Curve," Working Paper Series 2102, Department of Economics, Norwegian University of Science and Technology.
    8. Calzolari, Giorgio & Panattoni, Lorenzo, 1983. "Hessian and approximated Hessian matrices in maximum likelihood estimation: a Monte Carlo study," MPRA Paper 28847, University Library of Munich, Germany.
    9. David F. Hendry & Peter C.B. Phillips, 2017. "John Denis Sargan at the London School of Economics," Cowles Foundation Discussion Papers 2082, Cowles Foundation for Research in Economics, Yale University.
    10. Jansson, Leif & Mellander, Erik, 1984. "CONRAD – A Maximum Likelihood Program for Estimation of Simultaneous Equations Models that are Non-Linear in the Parameters," Working Paper Series 131, Research Institute of Industrial Economics.
    11. Bårdsen, Gunnar & Jansen, Eilev S. & Nymoen, Ragnar, 2003. "Testing the New Keynesian Phillips curve," Memorandum 18/2002, Oslo University, Department of Economics.
    12. Hendry, David F., 1984. "Monte carlo experimentation in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 16, pages 937-976, Elsevier.
    13. Palm, F.C., 1981. "Structural econometric modelling and time series analysis towards an integrated approach," Serie Research Memoranda 0004, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    14. Hatemi-J, Abdulnasser, 2004. "Multivariate tests for autocorrelation in the stable and unstable VAR models," Economic Modelling, Elsevier, vol. 21(4), pages 661-683, July.
    15. Moosa, Imad A., 1997. "A Cross-Country Comparison of Okun's Coefficient," Journal of Comparative Economics, Elsevier, vol. 24(3), pages 335-356, June.
    16. Turkington, Darrell A., 1998. "Efficient estimation in the linear simultaneous equations model with vector autoregressive disturbances," Journal of Econometrics, Elsevier, vol. 85(1), pages 51-74, July.
    17. Calzolari, Giorgio & Panattoni, Lorenzo, 1984. "Evaluating Forecast Uncertainty in Econometric Models: The Effect of Alternative Estimators of Maximum Likelihood Covariance Matrix," MPRA Paper 28806, University Library of Munich, Germany.
    18. C. R. McKenzie & Michael McAleer, 2001. "Comparing Tests of Autoregressive Versus Moving Average Errors in Regression Models Using Bahadur's Asymptotic Relative Efficiency," ISER Discussion Paper 0537, Institute of Social and Economic Research, The University of Osaka.
    19. vdr Leeuw, J.L., 1997. "Maximum Likelihood Estimation of Exact ARMA Models," Other publications TiSEM a1cdd9b8-93d9-460c-a0c9-1, Tilburg University, School of Economics and Management.
    20. Jan F. Kiviet, 1986. "On the Rigour of Some Misspecification Tests for Modelling Dynamic Relationships," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 241-261.

    More about this item

    Keywords

    Financial Economics;

    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:ags:queddp:275148. 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: AgEcon Search (email available below). General contact details of provider: https://edirc.repec.org/data/qedquca.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.