Some asymptotic properties of the least squares estimators of a polynomial regression with a heteroskedastic error

We investigate asymptotic properties of the least squares estimators of the coefficients in a polynomial regression when the error is heteroskedastic and its variance increases with time varying. First, we show the weak consistency of the estimators under some assumptions on the covariance structure of the error, Second, the consistency of an estimator of the variance of the error is studied. Finally, we examine the asymptotic efficiency of the estimators of the coefficients when the errors are uncorrelated.