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Title: Maximum likelihood estimation for noninvertible ARMA processes with stable distribution innovation process Authors:  Juho Nyholm - University of Helsinki (Finland) [presenting]
Abstract: The focus is on properties of a maximum likelihood estimators of the nonivertible ARMA process with innovation process in the class of stable distributions. We restrict the analysis to non-Gaussian stable distributions that do not necessarily have finite second moments. We show that there is a non-standard distribution for the sequence of $n^{1/\alpha}$-consistent estimators that are obtained as maximizers of the likelihood function. The non-standard limiting distribution of the ML estimator is obtained as a maximizer of a random function. Results are applied to economic time series data and we show that relaxing the standard assumptions on Gaussianity and invertibility may lead to better fit and alter the conclusions drawn from the data.