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

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  • 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
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    References listed on IDEAS

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    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. Hendry, David F, 1974. "Maximum Likelihood Estimation of Systems of Simultaneous Regression Equations with Errors Generated by a Vector Autoregressive Process: A Correction," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 260-260, February.
    7. 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.
    8. Pagan, Adrian, 1974. "A Generalised Approach to the Treatment of Autocorrelation," Australian Economic Papers, Wiley Blackwell, vol. 13(23), pages 267-280, December.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
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