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.
Abrahamse, A. P. J. and Koerts, J. (1971). New estimates of disturbances in regression analysis. Journal of the American Statistical Association, 66, 71–74.
Beach, C. M. and MacKinnon, J. G. (1978a). A maximum likelihood procedure for regression with autocorrelated errors. Econometrica, 46, 51–58.
Beach, C. M. and MacKinnon, J. G. (1978b). Full maximum likelihood estimation of second-order autoregressive error models. Journal of Econometrics, 7, 187–198.
Box, G. E. P. and Jenkins, G. M. (1970). Time Series Analysis, Forecasting and Control. San Francisco: Holden Day.
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.
Carlson, J. A. (1977). A study of price forecasts. Annals of Economic and Social Measurements, 6, 27–56.
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.
Dhrymes, P. J. (1971). Distributed Lags: Problems of Estimation and Formulation. San Francisco: Holden Day.
Durbin, J. (1960). Estimation of parameters in time series regression models. Journal of the Royal Statistical Society, B, 22, 139–153.
Durbin, J. and Watson, G. S. (1950). Testing for serial correlation in least squares regression-I. Biometrika, 37, 409–428.
Durbin, J. and Watson, G. S. (1951). Testing for serial correlation in least squares regression—II. Biometrika, 38, 159–178.
Durbin, J. and Watson, G. S. (1971). Test for serial correlation in least squares regression—III. Biometrika, 58, 1–42.
Farebrother, R. W. (1980). The Durbin-Watson test for serial correlation when there is no intercept in the regression. Econometrica, 48, 1553–1563.
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.
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.
Fuller, W. A. (1976). Introduction to Statistical Time Series. New York: Wiley.
Geary, R. C. (1970). Relative efficiency of count of sign changes for assessing residual autoregression in least squares regression. Biometrika, 57, 123–127.
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.
Hannan, E. J. and Terrell, R. D. (1968). Testing for serial correlation after least squares regression. Econometrica, 36, 133–150.
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.
Henshaw, R. C. (1966). Testing single-equation least-squares regression models for autocorrelated disturbances. Econometrica, 34, 646–660.
Hildreth, C. and Lu, J. Y. (1960). Demand relationships with autocorrelated disturbances. Michigan State University Agricultural Experiment Station Bulletin 276, East Lansing, Michigan.
Imhof, J. P. (1961). Computing the distribution of quadratic forms in normal variables. Biometrika, 48, 419–426.
Johnston, J. (1972). Econometric Methods, 2nd ed. New York: McGraw-Hill.
Koerts, J. and Abrahamse, A. P. J. (1968). On the power of the BLUS procedure. Journal of the American Statistical Association, 63, 1227–1236.
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.
Maddala, G. S. (1977). Econometrics. New York: McGraw-Hill.
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.
Malinvaud, E. (1970). Statistical Methods in Econometrics. Amsterdam: North-Holland.
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.
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.
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.
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.
Prais, S. J. and Winsten, C. B. (1954). Trend estimators and serial correlation. Cowles Commission Discussion Paper No. 383, Chicago.
Press, S. J. (1972). Applied Multivariate Analysis. New York: Holt, Rinehart, & Winston.
Rao, C. R. (1973). Linear Statistical Inference and Its Applications, 2nd ed. New York: Wiley.
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.
Rothenberg, T. J. (1973). Efficient Estimation with A Priori Information. Cowles Commission Monograph No. 23. New Haven, CT.: Yale University Press.
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.
Savin, N. E. and White, K. J. (1978). Testing for autocorrelation with missing observations. Econometrica, 46, 59–67.
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.
Theil, H. (1965). The analysis of disturbances in regression analysis. Journal of the American Statistical Association, 60, 1067–1079.
Theil, H. (1971). Principles of Econometrics. New York: Wiley.
Theil, H. and Nagar, A. L. (1961). Testing the independence of regression disturbances. Journal of the American Statistical Association, 56, 793–806.
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.
Tiao, G. C. and Ali, M. M. (1971). Analysis of correlated random effects: linear model with two random components. Biometrika, 58, 37–51.
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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
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