Maximum likelihood estimation of a noninvertible ARMA model with autoregressive conditional heteroskedasticity

Authors:
Mika Meitz;Pentti Saikkonen
Affiliations:
Department of Economics, Koç University, Rumelifeneri Yolu, 34450 Sariyer, Istanbul, Turkey;Department of Mathematics and Statistics, University of Helsinki, P.O.Box 68, FIN-00014 University of Helsinki, Finland
Venue:
Journal of Multivariate Analysis
Year:
2013

Citing 4
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Abstract

We consider maximum likelihood estimation of a particular noninvertible ARMA model with autoregressive conditionally heteroskedastic (ARCH) errors. The model can be seen as an extension to the so-called all-pass models in that it allows for autocorrelation and for more flexible forms of conditional heteroskedasticity. These features may be attractive especially in economic and financial applications. Unlike in previous literature on maximum likelihood estimation of noncausal and/or noninvertible ARMA models and all-pass models, our estimation theory does allow for Gaussian innovations. We give conditions under which a strongly consistent and asymptotically normally distributed solution to the likelihood equations exists, and we also provide a consistent estimator of the limiting covariance matrix.