EFFICIENCY OF ORDINARY LEAST SQUARES IN REGRESSION MODELS WITH AUTOCORRELATED DISTURBANCES IN A CLASSICAL LINEAR STATISTICAL MODEL.

Bartholomew A Uchendu¹, Uzoma Phillip Uche²and Duruojinkeya Prisca³

Department of Maths/Statistics,

Federal Polytechnic, Nekede, Owerri, Nigeria.

Email: uchendubartholomew@yahoo.com, uzomaphilip@gmail.com, priscaudo1@gmail.com

ABSTRACT

The illustrative values of the asymptotic efficiency for the selected values of ρ and λ shows that, when ρ and λ are both positive, it is clear, that ρ is the dominant parameter. Efficiency declines from 90 percent to about, 10 percent as ρ rises from 0.2 to 0.9, with variations in λ having relatively minor effect. The diagonal entries are equal to those in the first row of table (2) since if λ = 0 or if ρ = λ, the efficiency measure simplified to (1 – ρ²)/(1 + ρ²). Looking at the left hand side of the table, the efficiencies are symmetrical across the first row where the x_t series are random. The remaining rows show that λ now exerts a much stronger effect and that the combination of a positive λ and negative ρ can moderate the dramatic declines in efficiency shown in the right – hand side of the table. These calculations are of course, only illustrative, but, they indicate the possibility of a serious loss in efficiency if Ordinary Least Squares is applied in the context of autocorrelated disturbances.

Keywords: Efficiency, Ordinary Least Squares, Autocorrelated disturbances.