  This paper introduces new techniques for estimating, identifying and
simulating mixed causal-noncausal invertible-noninvertible models. We propose a
framework that integrates high-order cumulants, merging both the spectrum and
bispectrum into a single estimation function. The model that most adequately
represents the data under the assumption that the error term is i.i.d. is
selected. Our Monte Carlo study reveals unbiased parameter estimates and a high
frequency with which correct models are identified. We illustrate our strategy
through an empirical analysis of returns from 24 Fama-French emerging market
stock portfolios. The findings suggest that each portfolio displays noncausal
dynamics, producing white noise residuals devoid of conditional heteroscedastic
effects.
