Non‐causal and non‐invertible ARMA models: Identification, estimation and application in equity portfolios

The mixed causal‐non‐causal invertible‐non‐invertible autoregressive moving‐average (MARMA) models have the advantage of incorporating roots inside the unit circle, thus adjusting the dynamics of financial returns that depend on future expectations. This article introduces new techniques for estimating, identifying and simulating MARMA models. Although the estimation of the parameters is done using second‐order moments, the identification relies on the existence of high‐order dynamics, captured in the high‐order spectral densities and the correlation of the squared residuals. A comprehensive Monte Carlo study demonstrated the robust performance of our estimation and identification methods. We propose an empirical application to 24 portfolios from emerging markets based on the factors: size, book‐to‐market, profitability, investment and momentum. All portfolios exhibited forward‐looking behavior, showing significant non‐causal and non‐invertible dynamics. Moreover, we found the residuals to be uncorrelated and independent, with no trace of conditional volatility.