A strictly stationary, $N$-tuplewise independent counterexample to the Central Limit Theorem

Abstract

For an arbitrary integer $N\ge 2$, this paper gives the construction of a strictly stationary (and ergodic), $N$-tuplewise independent sequence of (nondegenerate) bounded random variables such that the Central Limit Theorem fails to hold. The sequence is in part an adaptation of a nonstationary example with similar properties constructed by one of the authors (ARP) in a paper published in 1998.