Heteroskedasticity And Autocorrelation Efficient (HAE) Estimation And Pivots For Jointly Evolving Series

A new two-way map between time domain and numerical magnitudes or values domain (v-dom) provides a new solution to heteroscedasticity. Since sorted logs of squared fitted residuals are monotonic in the v-dom, one obtain a parsimonious fit there. Two theorems prove consistency, asymptotic normality, efficiency and specificationrobustness, supplemented by a simulation. Since Dufour's (1997) impossibility theorems show how confidence intervals from Wald-type tests can have zero coverage, the author suggests Godambe pivot functions (GPF) with good finite sample coverage and distribution-free robustness. The author uses the Frisch-Waugh theorem and the scalar GPF to construct new confidence intervals for regression parameters and apply Vinod's (2004, 2006) maximum entropy bootstrap. The author uses Irving Fisher's model for interest rates and Keynesian consumption function for illustration.