ASYMPTOTIC-DISTRIBUTION OF STATISTICS IN TIME-SERIES

Verifiable conditions are given for the validity of formal Edgeworth expansions for the distribution of sums X(1) + ... + X(n), where X(i) = F(Z(i), ..., Z(i + p - 1)) and Z(1),Z(2), ... is a strict sense stationary sequence that can be written as Z(j) = g(epsilon(j-k): k greater than or equal to 0) with an lid sequence (epsilon(i)) of innovations. These models include nonlinear functions of ARMA processes (Z(i)) as well as certain nonlinear AR processes. The results apply to many statistics in (nonlinear) time series models.