Maximum Likelihood Estimation of a Noninvertible ARMA Model with Autoregressive Conditional Heteroskedasticity

Mika Meitz () and Pentti Saikkonen
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Pentti Saikkonen: Department of Mathematics and Statistics, University of Helsinki

Koç University-TUSIAD Economic Research Forum Working Papers from Koc University-TUSIAD Economic Research Forum

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 so-called all-pass models in that it allows for autocorrelation and for more fl exible 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.

Keywords: Maximum likelihood estimation; autoregressive moving average; ARMA; autoregressive conditional heteroskedasticity; ARCH; noninvertible; noncausal; all-pass; nonminimum phase. (search for similar items in EconPapers)
JEL-codes: C22 C51 (search for similar items in EconPapers)
Pages: 45 pages
Date: 2012-09
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Maximum likelihood estimation of a noninvertible ARMA model with autoregressive conditional heteroskedasticity (2013)
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