Maximum Likelihood Estimation of a Noninvertible ARMA Model with Autoregressive Conditional Heteroskedasticity
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Koc University-TUSIAD Economic Research Forum in its series Koç University-TUSIAD Economic Research Forum Working Papers with number 1226.
Length: 45 pages
Date of creation: Sep 2012
Date of revision:
Maximum likelihood estimation; autoregressive moving average; ARMA; autoregressive conditional heteroskedasticity; ARCH; noninvertible; noncausal; all-pass; nonminimum phase.;
Other versions of this item:
- Meitz, Mika & Saikkonen, Pentti, 2013. "Maximum likelihood estimation of a noninvertible ARMA model with autoregressive conditional heteroskedasticity," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 227-255.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-30 (All new papers)
- NEP-ECM-2012-09-30 (Econometrics)
- NEP-ETS-2012-09-30 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Meitz, Mika & Saikkonen, Pentti, 2011.
"Parameter Estimation In Nonlinear Ar–Garch Models,"
Cambridge University Press, vol. 27(06), pages 1236-1278, December.
- Mika Meitz & Pentti Saikkonen, 2008. "Parameter estimation in nonlinear AR-GARCH models," Economics Series Working Papers 396, University of Oxford, Department of Economics.
- 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.
- Mika Meitz & Pentti Saikkonen, 2010. "Parameter estimation in nonlinear AR–GARCH models," KoÃ§ University-TUSIAD Economic Research Forum Working Papers 1002, Koc University-TUSIAD Economic Research Forum.
- Mika Meitz & Pentti Saikkonen, 2008. "Parameter Estimation in Nonlinear AR-GARCH Models," Economics Working Papers ECO2008/25, European University Institute.
- Lanne, Markku & Luoto, Jani & Saikkonen, Pentti, 2012.
"Optimal forecasting of noncausal autoregressive time series,"
International Journal of Forecasting,
Elsevier, vol. 28(3), pages 623-631.
- Lanne, Markku & Luoto, Jani & Saikkonen, Pentti, 2010. "Optimal Forecasting of Noncausal Autoregressive Time Series," MPRA Paper 23648, University Library of Munich, Germany.
- Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2012.
"Testing for predictability in a noninvertible ARMA model,"
37151, University Library of Munich, Germany.
- Markku Lanne & Mika Meitz & Pentti Saikkonen, 2012. "Testing for Predictability in a Noninvertible ARMA Model," KoÃ§ University-TUSIAD Economic Research Forum Working Papers 1225, Koc University-TUSIAD Economic Research Forum.
- Saikkonen, Pentti & Sandberg , Rickard, 2013. "Testing for a unit root in noncausal autoregressive models," Research Discussion Papers 26/2013, Bank of Finland.
- Gospodinov, Nikolay & Ng, Serena, 2013. "Minimum distance estimation of possibly non-invertible moving average models," Working Paper 2013-11, Federal Reserve Bank of Atlanta.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sumru Oz).
If references are entirely missing, you can add them using this form.