Velasco, CarlosLobato García-Miján, Ignacio2022-04-012022-04-012018-04-01Velasco, C., & Lobato, I. N. (2018). Frequency domain minimum distance inference for possibly noninvertible and noncausal ARMA models. The Annals of Statistics, 46(2), pp. 555-5790090-5364https://hdl.handle.net/10016/34510This article introduces frequency domain minimum distance procedures for performing inference in general, possibly non causal and/or noninvertible, autoregressive moving average (ARMA) models. We use information from higher order moments to achieve identification on the location of the roots of the AR and MA polynomials for non-Gaussian time series. We propose a minimum distance estimator that optimally combines the information contained in second, third, and fourth moments. Contrary to existing estimators, the proposed one is consistent under general assumptions, and may improve on the efficiency of estimators based on only second order moments. Our procedures are also applicable for processes for which either the third or the fourth order spectral density is the zero function.eng© 2018 Institute of Mathematical StatisticsHigher-order momentsHigher-order spectraNonminimum phaseWhittle estimate.research articleEconomía10.1214/17-AOS1560open access5552579ANNALS OF STATISTICS46AR/0000021455