Non Spherical Disturbances - Econometrics - Lecture Notes, Study notes of Econometrics and Mathematical Economics

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Non-Spherical Disturbance Heteroskedasticity and Autocorrelation The Generalized Linear Regression Model The general linear regression model is y=XB+e sumption A. E(e|X)=0 |X) = 072 Assumption Ail: E( a positive definite matrix. Two cases we shall consider in detail are heteroskedas. where 2 is icity and autocorrelation. Disturbances are heteroskedastic wheu they have different variances. Heteruskedas- ticity usually arises in cross-section data where the scale of the dependent variable and the explanatory power of the model tend to vary over observations. The errors are still so 970 would be assimned to be uncorrelated across observations. foR 0 0 6 0 0 , (cross-section cata) 0 0 \ s data. Economic time series often Autocorrelation is usually found in time-scri display a “tuemory” in that variation around the regression fuuction is uot independent from one period to the next: B(sie4) # Ui, for t # s. Time-series data usually are homoskedastic, so 67Q could be, |p| < 1, (time-series data)