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

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  • Mika Meitz

    ()
    (Department of Economics, Koç University)

  • Pentti Saikkonen

    ()
    (Department of Mathematics and Statistics, University of Helsinki)

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.

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Bibliographic Info

Paper provided by Koc University-TUSIAD Economic Research Forum in its series Koç University-TUSIAD Economic Research Forum Working Papers with number 1226.

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Length: 45 pages
Date of creation: Sep 2012
Date of revision:
Handle: RePEc:koc:wpaper:1226

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Keywords: Maximum likelihood estimation; autoregressive moving average; ARMA; autoregressive conditional heteroskedasticity; ARCH; noninvertible; noncausal; all-pass; nonminimum phase.;

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References

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  1. Mika Meitz & Pentti Saikkonen, 2008. "Parameter estimation in nonlinear AR-GARCH models," CREATES Research Papers 2008-30, School of Economics and Management, University of Aarhus.
  2. Lanne, Markku & Luoto, Jani & Saikkonen, Pentti, 2010. "Optimal Forecasting of Noncausal Autoregressive Time Series," MPRA Paper 23648, University Library of Munich, Germany.
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Cited by:
  1. Gospodinov, Nikolay & Ng, Serena, 2013. "Minimum distance estimation of possibly non-invertible moving average models," Working Paper 2013-11, Federal Reserve Bank of Atlanta.
  2. Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2012. "Testing for predictability in a noninvertible ARMA model," MPRA Paper 37151, University Library of Munich, Germany.
  3. Saikkonen, Pentti & Sandberg , Rickard, 2013. "Testing for a unit root in noncausal autoregressive models," Research Discussion Papers 26/2013, Bank of Finland.

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