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Statistica Sinica 27 (2017), 519-533

QUENCHED CENTRAL LIMIT THEOREMS
FOR A STATIONARY LINEAR PROCESS
Dalibor Volný and Michael Woodroofe
Université de Rouen - Normandie and University of Michigan

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.

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