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

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  • Meitz, Mika
  • Saikkonen, Pentti

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 114 (2013)
Issue (Month): C ()
Pages: 227-255

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Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:227-255

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  1. Mika Meitz & Pentti Saikkonen, 2008. "Parameter estimation in nonlinear AR-GARCH models," Economics Series Working Papers 396, University of Oxford, Department of Economics.
  2. Lanne, Markku & Luoto, Jani & Saikkonen, Pentti, 2012. "Optimal forecasting of noncausal autoregressive time series," International Journal of Forecasting, Elsevier, Elsevier, vol. 28(3), pages 623-631.
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Cited by:
  1. Markku Lanne & Mika Meitz & Pentti Saikkonen, 2012. "Testing for Predictability in a Noninvertible ARMA Model," Koç University-TUSIAD Economic Research Forum Working Papers, Koc University-TUSIAD Economic Research Forum 1225, Koc University-TUSIAD Economic Research Forum.
  2. Saikkonen, Pentti & Sandberg , Rickard, 2013. "Testing for a unit root in noncausal autoregressive models," Research Discussion Papers 26/2013, Bank of Finland.
  3. Gospodinov, Nikolay & Ng, Serena, 2013. "Minimum distance estimation of possibly non-invertible moving average models," Working Paper, Federal Reserve Bank of Atlanta 2013-11, Federal Reserve Bank of Atlanta.

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