Uniform inference across the recurrence boundary

Establish uniform statistical inference for the state-weighted weighted least-squares intercept across the recurrence boundary at \(\tau=1\), where the residual pivot has different limiting distributions at and away from the boundary.

Background

The paper derives asymptotic inference for the state-weighted weighted least-squares intercept in the strict-recurrence regime $0<\tau<1$, at the recurrence boundary $\tau=1$, and in the transient regime $\tau>1$. The resulting residual pivot is asymptotically standard normal away from the boundary but has the nonnormal limit $(1-U)/\sqrt{T}$ at $\tau=1$.

Because these limiting laws differ discontinuously across the boundary, the fixed-regime confidence procedures established in the paper do not provide uniform coverage when the recurrence parameter approaches or crosses $\tau=1$. Developing an inference method with uniform validity across this transition is therefore left unresolved.