Ch.8 Nonspherical Disturbance This chapter will assume that the full ideal conditions hold except that the covari- ance matrix of the disturbance, i.e. E(EE)=02Q2, where Q is not the identity matrix. In particular, Q may be nondiagonal and / or have unequal diagonal ele- ments Two cases we shall consider in details are heteroscedasticity and auto- correlation. Disturbance are heteroscedastic when they have different variance Heteroscedasticity usually arise in cross-section data where the scale of the de- pendent variable and the explanatory power of the model tend to vary across observations. The disturbance are still assumed to be uncorrelated across obser vation, so an would be g2 0 2g2 Autocorrelation is usually found in time-series data. Economic time-series often display a"memory"in that variation around the regression function is not independent from one period to the next. Time series data are usually ho- moscedasticity, so aQ2 would be 1p1 PT-1 Pr-2 In recent studies, panel data sets, constituting of cross sections observed at several points in time, have exhibited both characteristics. The next three chap- ter examines in details specific types of generalized regression models Our earlier results for the classical mode: will have to be modified. We first consider the consequence of the more general model for the least squares estima- torsCh. 8 Nonspherical Disturbance This chapter will assume that the full ideal conditions hold except that the covari￾ance matrix of the disturbance , i.e. E(εε0 ) = σ 2Ω, where Ω is not the identity matrix. In particular, Ω may be nondiagonal and/or have unequal diagonal ele￾ments. Two cases we shall consider in details are heteroscedasticity and auto￾correlation. Disturbance are heteroscedastic when they have different variance. Heteroscedasticity usually arise in cross-section data where the scale of the de￾pendent variable and the explanatory power of the model tend to vary across observations. The disturbance are still assumed to be uncorrelated across obser￾vation, so σ 2Ω would be σ 2Ω =         σ 2 1 0 . . . 0 0 σ 2 2 . . . 0 . . . . . . . . . . . . . . . . . . 0 0 . . . σ 2 T         . Autocorrelation is usually found in time-series data. Economic time-series often display a ”memory” in that variation around the regression function is not independent from one period to the next. Time series data are usually ho￾moscedasticity, so σ 2Ω would be σ 2Ω = σ 2         1 ρ1 . . . ρT −1 ρ1 1 . . . ρT −2 . . . . . . . . . . . . . . . . . . ρT −1 ρT −2 . . . 1         . In recent studies, panel data sets, constituting of cross sections observed at several points in time, have exhibited both characteristics. The next three chap￾ter examines in details specific types of generalized regression models. Our earlier results for the classical mode; will have to be modified. We first consider the consequence of the more general model for the least squares estima￾tors. 1