Semiparametric ARCH Models: An Estimating Function Approach
AbstractWe introduce the method of estimating functions to study the class of autoregressive conditional heteroscedasticity (ARCH) models. We derive the optimal estimating functions by combining linear and quadratic estimating functions. The resultant estimators are more efficient than the quasi-maximum likelihood estimator. If the assumption of conditional normality is imposed, the estimator obtained by using the theory of estimating functions is identical to that obtained by using the maximum likelihood method in finite samples. The relative efficiencies of the estimating function (EF) approach in comparison with the quasi-maximum likelihood estimator are developed. We illustrate the EF approach using a univariate GARCH(1,1) model with conditional normal. Student-t, and gamma distributions. The efficiency benefits of the EF approach relative to the quasi-maximum likelihood approach are substantial for the gamma distribution with large skewness. Simulation analysis shows that the finite-sample properties of the estimators from the EF approach are attractive. EF estimators tend to display less bias and root mean squared error than the quasi-maximum likelihood estimator. The efficiency gains are substantial for highly nonnormal distributions. An example demonstrates that implementation of the method is straightforward.
Download InfoTo our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
Bibliographic InfoArticle provided by American Statistical Association in its journal Journal of Business and Economic Statistics.
Volume (Year): 18 (2000)
Issue (Month): 2 (April)
Contact details of provider:
Web page: http://www.amstat.org/publications/jbes/index.cfm?fuseaction=main
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Bera, Anil K. & Bilias, Yannis, 2002. "The MM, ME, ML, EL, EF and GMM approaches to estimation: a synthesis," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 51-86, March.
- Allen, David & Ng, K.H. & Peiris, Shelton, 2013. "The efficient modelling of high frequency transaction data: A new application of estimating functions in financial economics," Economics Letters, Elsevier, vol. 120(1), pages 117-122.
- Verhoeven, Peter & McAleer, Michael, 2004.
"Fat tails and asymmetry in financial volatility models,"
Mathematics and Computers in Simulation (MATCOM),
Elsevier, vol. 64(3), pages 351-361.
- Peter Verhoeven & Michael McAleer, 2003. "Fat Tails and Asymmetry in Financial Volatility Models," CIRJE F-Series CIRJE-F-211, CIRJE, Faculty of Economics, University of Tokyo.
- Allen, David & Ng, K.H. & Peiris, Shelton, 2013. "Estimating and simulating Weibull models of risk or price durations: An application to ACD models," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 214-225.
- Park, Sung Y. & Bera, Anil K., 2009. "Maximum entropy autoregressive conditional heteroskedasticity model," Journal of Econometrics, Elsevier, vol. 150(2), pages 219-230, June.
- repec:wyi:journl:002099 is not listed on IDEAS
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.