Contents
What are the bad consequences of Heteroskedasticity?
Heteroskedasticity has serious consequences for the OLS estimator. Although the OLS estimator remains unbiased, the estimated SE is wrong. Because of this, confidence intervals and hypotheses tests cannot be relied on. In addition, the OLS estimator is no longer BLUE.
What are the two major consequences of Heteroskedasticity?
The OLS estimators and regression predictions based on them remains unbiased and consistent. The OLS estimators are no longer the BLUE (Best Linear Unbiased Estimators) because they are no longer efficient, so the regression predictions will be inefficient too.
What are the consequences of heteroscedasticity in regression?
Consequences of Heteroscedasticity The OLS estimators and regression predictions based on them remains unbiased and consistent. The OLS estimators are no longer the BLUE (Best Linear Unbiased Estimators) because they are no longer efficient, so the regression predictions will be inefficient too.
Why does heteroscedasticity occur in large datasets?
Heteroscedasticity, also spelled heteroskedasticity, occurs more often in datasets that have a large range between the largest and smallest observed values. While there are numerous reasons why heteroscedasticity can exist, a common explanation is that the error variance changes proportionally with a factor.
Which is a heteroscedastic model with independent errors?
In the last set of notes, we considered a model Y = Xβ + ϵ, ϵ ∼ N(0, W − 1) where W − 1 = σ2 ⋅ diag(V1, …, Vn). This model has independent errors, but of different variance: a heteroscedastic model. We saw that by defining ˜Y = W1 / 2Y, ˜X = W1 / 2X we transformed our original model to more familiar model: ˜Y = ˜Xβ + ε, ε ∼ N(0, σ2I).
The model of the variance that we will consider today is a model where the errors are correlated. In the random effects model, outcomes within groups were correlated. Other regression applications also have correlated outcomes (i.e. errors). Common examples of this type of errors occur in time series data, a common model for financial applications.