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Autocorrelation

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Advanced Econometric Methods

Abstract

In this chapter we deal with statistical inference in the linear model when it is not appropriate to assume that the random disturbances are uncorrelated. The phenomenon of correlated errors in linear regression models involving time series data is called autocorrelation. Results to follow show that there is much to gain and little to lose by considering alternatives to the independent error assumption of the classical linear regression model. These results are discussed in the context of feasible generalized least squares of Chapter 8.

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References

  • Abrahamse, A. P. J. and Koerts, J. (1969). A comparison of the Durbin-Watson test and the Blus test. Journal of the American Statistical Association, 64, 938–948.

    Article  Google Scholar 

  • Abrahamse, A. P. J. and Koerts, J. (1971). New estimates of disturbances in regression analysis. Journal of the American Statistical Association, 66, 71–74.

    Article  Google Scholar 

  • Beach, C. M. and MacKinnon, J. G. (1978a). A maximum likelihood procedure for regression with autocorrelated errors. Econometrica, 46, 51–58.

    Article  Google Scholar 

  • Beach, C. M. and MacKinnon, J. G. (1978b). Full maximum likelihood estimation of second-order autoregressive error models. Journal of Econometrics, 7, 187–198.

    Article  Google Scholar 

  • Box, G. E. P. and Jenkins, G. M. (1970). Time Series Analysis, Forecasting and Control. San Francisco: Holden Day.

    Google Scholar 

  • Box, G. E. P. and Pierce, D. A. (1970). Distribution of residual autocorrelations in autoregressive moving average time series models. Journal of the American Statistical Association, 65, 1509–1526.

    Article  Google Scholar 

  • Carlson, J. A. (1977). A study of price forecasts. Annals of Economic and Social Measurements, 6, 27–56.

    Google Scholar 

  • Cochrane, D. and Orcutt, G. H. (1949). Application of least squares regressions to relationships containing autocorrelated error terms. Journal of the American Statistical Association, 44, 32–61.

    Google Scholar 

  • Dhrymes, P. J. (1971). Distributed Lags: Problems of Estimation and Formulation. San Francisco: Holden Day.

    Google Scholar 

  • Durbin, J. (1960). Estimation of parameters in time series regression models. Journal of the Royal Statistical Society, B, 22, 139–153.

    Google Scholar 

  • Durbin, J. and Watson, G. S. (1950). Testing for serial correlation in least squares regression-I. Biometrika, 37, 409–428.

    Google Scholar 

  • Durbin, J. and Watson, G. S. (1951). Testing for serial correlation in least squares regression—II. Biometrika, 38, 159–178.

    Google Scholar 

  • Durbin, J. and Watson, G. S. (1971). Test for serial correlation in least squares regression—III. Biometrika, 58, 1–42.

    Google Scholar 

  • Farebrother, R. W. (1980). The Durbin-Watson test for serial correlation when there is no intercept in the regression. Econometrica, 48, 1553–1563.

    Article  Google Scholar 

  • Fomby, T. B. and Guilkey, D. K. (1978). On choosing the optimal level of significance for the Durbin-Watson test and the Bayesian alternative. Journal of Econometrics, 8, 203–214.

    Article  Google Scholar 

  • Frohman, D. A., Laney, L. O., and Willet, T. D. (1981). Uncertainty costs of high inflation. Voice (of the Federal Reserve Bank of Dallas), July, 1–9.

    Google Scholar 

  • Fuller, W. A. (1976). Introduction to Statistical Time Series. New York: Wiley.

    Google Scholar 

  • Geary, R. C. (1970). Relative efficiency of count of sign changes for assessing residual autoregression in least squares regression. Biometrika, 57, 123–127.

    Article  Google Scholar 

  • Habibagahi, H. and Pratschke, J. L. (1972). A comparison of the power of the von Neumann ratio, Durbin-Watson, and Geary tests. Review of Economics and Statistics, 54, 179–185.

    Article  Google Scholar 

  • Hannan, E. J. and Terrell, R. D. (1968). Testing for serial correlation after least squares regression. Econometrica, 36, 133–150.

    Article  Google Scholar 

  • Harrison, M. J. (1975). The power of the Durbin-Watson and Geary tests: comment and further evidence. Review of Economics and Statistics, 57, 377–379.

    Article  Google Scholar 

  • Henshaw, R. C. (1966). Testing single-equation least-squares regression models for autocorrelated disturbances. Econometrica, 34, 646–660.

    Article  Google Scholar 

  • Hildreth, C. and Lu, J. Y. (1960). Demand relationships with autocorrelated disturbances. Michigan State University Agricultural Experiment Station Bulletin 276, East Lansing, Michigan.

    Google Scholar 

  • Imhof, J. P. (1961). Computing the distribution of quadratic forms in normal variables. Biometrika, 48, 419–426.

    Google Scholar 

  • Johnston, J. (1972). Econometric Methods, 2nd ed. New York: McGraw-Hill.

    Google Scholar 

  • Koerts, J. and Abrahamse, A. P. J. (1968). On the power of the BLUS procedure. Journal of the American Statistical Association, 63, 1227–1236.

    Article  Google Scholar 

  • L’Espérance, W. L. and Taylor, D. (1975). The power of four tests of autocorrelation in the linear regression model. Journal of Econometrics, 3, 1–21.

    Article  Google Scholar 

  • Maddala, G. S. (1977). Econometrics. New York: McGraw-Hill.

    Google Scholar 

  • Magnus, J. R. (1978). Maximum likelihood estimation of the GLS model with GLS model with unknown parameters in the disturbance covariance matrix. Journal of Econometrics, 7, 281–312.

    Article  Google Scholar 

  • Malinvaud, E. (1970). Statistical Methods in Econometrics. Amsterdam: North-Holland.

    Google Scholar 

  • Nakamura, A. and Nakamura, M. (1978). On the impact of the tests for serial correlation upon the test of significance for the regression coefficient. Journal of Econometrics, 7, 199–210.

    Article  Google Scholar 

  • Oxley, L. T. and Roberts, C. T. (1982). Pitfalls in the application of the Cochrane-Orcutt technique. Oxford Bulletin of Economics and Statistics, 44, 227–240.

    Article  Google Scholar 

  • Pesaran, M. H. (1973). Exact maximum likelihood estimation of a regression equation with first-order moving-average error. Review of Economic Studies, 40, 529–536.

    Article  Google Scholar 

  • Pierce, D. A. (1971). Distribution of residual autocorrelations in the regression model with autoregressive-moving average errors. Journal of the Royal Statistical Society, B, 33, 140–146.

    Google Scholar 

  • Prais, S. J. and Winsten, C. B. (1954). Trend estimators and serial correlation. Cowles Commission Discussion Paper No. 383, Chicago.

    Google Scholar 

  • Press, S. J. (1972). Applied Multivariate Analysis. New York: Holt, Rinehart, & Winston.

    Google Scholar 

  • Rao, C. R. (1973). Linear Statistical Inference and Its Applications, 2nd ed. New York: Wiley.

    Book  Google Scholar 

  • Rao, P. and Griliches, Z. (1969). Small sample properties of several two-stage regression methods in the context of autocorrelated errors. Journal of the American Statistical Association, 64, 253–272.

    Article  Google Scholar 

  • Rothenberg, T. J. (1973). Efficient Estimation with A Priori Information. Cowles Commission Monograph No. 23. New Haven, CT.: Yale University Press.

    Google Scholar 

  • Savin, N. E. and White, K. J. (1977). The Durbin-Watson test for serial correlation with extreme sample sizes or many regressors. Econometrica, 45, 1989–1996.

    Article  Google Scholar 

  • Savin, N. E. and White, K. J. (1978). Testing for autocorrelation with missing observations. Econometrica, 46, 59–67.

    Article  Google Scholar 

  • Schmidt, P. and Guilkey, D. K. (1975). Some further evidence on the power of the Durbin-Watson and Geary tests. Review of Economics and Statistics, 57, 379–382.

    Article  Google Scholar 

  • Theil, H. (1965). The analysis of disturbances in regression analysis. Journal of the American Statistical Association, 60, 1067–1079.

    Article  Google Scholar 

  • Theil, H. (1971). Principles of Econometrics. New York: Wiley.

    Google Scholar 

  • Theil, H. and Nagar, A. L. (1961). Testing the independence of regression disturbances. Journal of the American Statistical Association, 56, 793–806.

    Article  Google Scholar 

  • Thornton, D. L. (1982). The appropriate autocorrelation transformation when the autocorrelation process has a finite past. Federal Reserve Bank of St. Louis Working Paper 82-002.

    Google Scholar 

  • Tiao, G. C. and Ali, M. M. (1971). Analysis of correlated random effects: linear model with two random components. Biometrika, 58, 37–51.

    Article  Google Scholar 

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© 1984 Springer Science+Business Media New York

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Fomby, T.B., Johnson, S.R., Hill, R.C. (1984). Autocorrelation. In: Advanced Econometric Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8746-4_10

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  • DOI: https://doi.org/10.1007/978-1-4419-8746-4_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96868-1

  • Online ISBN: 978-1-4419-8746-4

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