Spectral identification and estimation of mixed causal-noncausal invertible-noninvertible models

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.