Eftychia Lola and Spyridon D. Symeonides

Correspondence: Eftychia Lola, eftehialola@yahoo.gr

Department of Economics, University of Ioannina

pdf (434.12 Kb) | doi: https://doi.org/10.47260/bae/921

Abstract

In this paper we examine, from a theoretical viewpoint, the generalized normal linear regression model with disturbances that are simultaneously heteroskedastic and autoregressive. In particular, the error specification of the model is a mixture of Amemiya’s linear heteroscedasticity structure with a stationary first-order autoregressive process. Given that the heteroskedastic variances are functions of the first-order autocorrelation coefficient, the estimators used in applied research cannot properly distinguish the estimations of the heteroskedastic and autoregressive parameters of the model. To avoid this problem, we introduce a multi-step estimation procedure, which has mainly theoretical interest, and is not suggested as an alternative to the well-known heteroskedasticity and autocorrelation consistent estimation used in applied econometric research. This estimation procedure facilitates the derivation of two distinct, theoretically important, generalized linear models, one with heteroskedastic and another with first-order autoregressive error terms. These two distinct models can be used for the theoretical examination of the finite-sample distributional properties of the estimators of the heteroskedastic and autoregressive parameters.

Keywords:

  Linear regression model; autoregression; heteroskedasticity; consistent estimation

References

Abadir, K. M. and Magnus, J. R. (2002). Notation in Econometrics: A Proposal for A Standard. Econometrics Journal, 5:76–90.Amemiya, T. (1977). A Note on a Heteroscedastic Model. Journal of Econometrics, 6:365–370.Beach, C. M. and MacKinnon, J. G. (1978). A Maximum Likelihood Procedure for Regression with Autocorrelated Errors. Econometrica, 46(1):51–58.Cornish, E. A. and Fisher, R. A. (1937). Moments and Cumulants in The Specification of Distributions. Revue de l’ Institute International de Statistic, 4:1–14.Durbin, J. and Watson, G. S. (1950). Testing for Serial Correlation in Least Squares Regression: I. Biometrika, 37(3):409–428.Durbin, J. and Watson, G. S. (1951). Testing for Serial Correlation in Least Squares Regression: II. Biometrika, 38(1):159–177.Fisher, R. A. and Cornish, E. A. (1960). The Percentile Points of Distributions Having Known Cumulants. Technometrics, 2(2):209–225.Goldfeld, S. M. and Quandt, R. E. (1965). Some Tests for Homoscedasticity. Journal of the American Statistical Association, 60(310):539–547.Hill, G. W. and Davis, A. W. (1968). Generalized Asymptotic Expansions of Cornish-Fisher Type. The Annals of Mathematical Statistics, 39(4):1264–1273.MacKinnon, J. G. and White, H. (1985). Some Heteroskedasticity Consistent Covariance Matrix Estimators with Improved Finite Sample Properties. Journal of Econometrics, 29:305–325.Magdalinos, M. A. and Symeonides, S. D. (1995). Alternative Size Corrections for Some GLS Test Statistics: The Case of the AR(1) Model. Journal of Econometrics, 66(1–2):35–59.Newey, W. K. and West, K. (1987). A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica, 55:703–708.Prais, S. J. and Winsten, C. B. (1954). Trend Estimators and Serial Correlation. Cowles Commission Discussion Paper: Statistics No. 383.Rothenberg, T. J. (1984). Hypothesis Testing in Linear Models when the Error Covariance Matrix is Nonscalar. Econometrica, 52(4):827–842.Symeonides, S. D., Tzavalis, E., and Kandilorou, H. (2007). Cornish-Fisher Size Corrected t and F Statistics for the Linear Regression Model withHeteroskedastic Errors. In Philips, G. D. A. and Tzavalis, E., editors, The Refinement of Econometric Estimation and Test Procedures: FiniteSample and Asymptotic Analysis, pages 173–204. Cambridge University Press, Cambridge.Symeonides, S. D., Tzavalis, E., and Karavias, Y. (2016). Size Corrected Significance Tests in Seemingly Unrelated Regressions with Autocorrelated Errors. Journal of Time Series Econometrics, 9(1):1–40.Turkington, D. A. (2000). Generalised Vec Operators and the Seemingly Unrelated Regression Equations Model with Vector Correlated Disturbances. Journal of Econometrics, 99(2):225–53.White, H. (1980). A Heteroscedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroscedasticity. Econometrica, 48(4):817–838.