Time aggregation of mixed causal–noncausal models

We study systematic and flow aggregation of mixed causal-noncausal autoregressive models. We show that aggregation preserves noncausality and generates a moving average component. Monte Carlo simulations demonstrate that backward- and forward-looking behavior can be identified empirically for sufficiently large samples. • Aggregation of MAR models leads to ARMA models for which noncausality is preserved. • MA components generated upon aggregation are invertible-noninvertible. • Systematic and flow aggregation generally create different MA orders. • Model identification after aggregation may be adversely affected. • Simulations show that the identification problem vanishes for larger samples.