A Gls Estimation Of The Two-Way Random Effect Model With Double Autocorrelation

This thesis is a theoretical investigation of a frequently encountered econometric issue: the problem of autocorrelation. Under a two-way random effect context, we introduce serial correlation in the time-varying disturbances, leading to a double correlation framework. We analyze two major situations related to the structure of the error terms. The first one considers that the time-varying disturbances follow the same correlation pattern, with the same parameters. They are allowed to exhibit series such as the autoregressive of order 1 (hereafter AR(1)) or the moving-average of order 1 (hereafter MA(1)) processes. We also examined the case of unknown correlation. A detailed generalized least squares (hereafter GLS) procedure is deduced from the spectral decomposition of the variance-covariance matrix of the composite error term. A Feasible Generalized Least Squares (hereafter FGLS) approach is derived whatever the correlation status may be. The second error structure assumes that the time-varying disturbances can follow different correlation patterns. A general case of unknown serial correlation is considered, as well as the autoregressive and moving-average processes of order 1 models. We show that the variance-covariance matrix of the overall error term can always be written in a precise form, independently from the type of serial correlation. Once again, we deduce a GLS estimator from the inverse of this moment matrix. Underlying estimators are shown out and their asymptotic properties are studied. We find that the GLS estimator is asymptotically equivalent to a "within" estimator called the covariance estimator. Finally, a FGLS version is proposed.