A transformation that will circumvent the problem of autocorrelation in an error-component model

This paper derives a simple transformation which will transform serially correlated error-components disturbances into spherical disturbances. Although Ω and Ω^-1 are well known in the literature [see Lillard and Willis (1978)], the derivation of Ω ^{-1 2} has many advantages: (i) It transforms GLS into a WLS procedure and, therefore, simplifies the computation. (ii) It provides natural estimates of the variance components. (iii) The transformation obtained can be easily extended to handle more general error processes on the remainder disturbances. This is illustrated for the AR(1) model, AR(2) model, and the specialized AR(4) model for quarterly data. Also, for the AR(1) model, this transformation is extended to handle alternative assumptions on the initial observation. This paper also shows that Breusch's (1987) results on maximum-likelihood estimation for the random error-component model extend to the case of serial correlation in the remainder term. This suggests an iterative GLS procedure for obtaining the maximum-likelihood estimates.