Statistica Sinica 27 (2017), 519-533
Abstract: We establish a sufficient condition under which a central limit theorem for a a stationary linear process is quenched. We find a stationary linear process for which the Maxwell-Woodroofe’s condition is satisfied, , converges to the standard normal law, and the convergence is not quenched; the weak invariance principle does not hold.
Key words and phrases: Hannan condition, martingale differences, Maxwell-Woodrofe condition, quenched central limit theorem, stationary linear process, weak invariance principle.