Inconsistency of the MLE and inference based on weighted LS for LARCH models
This paper considers a class of finite-order autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be arbitrarily close to zero and to reach its minimum for non-zero innovations, and is appropriate for long memory modeling when infinite orders are allowed. However, the (quasi-)maximum likelihood estimator is, in general, inconsistent. A self-weighted least-squares estimator is proposed and is shown to be asymptotically normal. A score test for conditional homoscedasticity and diagnostic portmanteau tests are developed. Their performance is illustrated via simulation experiments. It is also investigated whether stock market returns exhibit some of the characteristic features of the linear ARCH model.
If 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
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.:
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
- Francq, Christian & Makarova, Svetlana & Zakoi[diaeresis]an, Jean-Michel, 2008. "A class of stochastic unit-root bilinear processes: Mixing properties and unit-root test," Journal of Econometrics, Elsevier, vol. 142(1), pages 312-326, January.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Sentana, Enrique, 1995.
"Quadratic ARCH Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 62(4), pages 639-61, October.
- Berkes, Istv n & Horv th, Lajos & Kokoszka, Piotr, 2003. "Asymptotics For Garch Squared Residual Correlations," Econometric Theory, Cambridge University Press, vol. 19(04), pages 515-540, August.
- Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, vol. 140(2), pages 849-873, October.
- Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-58, February.
- Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
- Liudas Giraitis, 2004. "LARCH, Leverage, and Long Memory," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 177-210.
- Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
- Beran, Jan, 2006. "On location estimation for LARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1766-1782, September.
- Horv th, Lajos & Kokoszka, Piotr, 2001. "LARGE SAMPLE DISTRIBUTION OF WEIGHTED SUMS OF ARCH(p) SQUARED RESIDUAL CORRELATIONS," Econometric Theory, Cambridge University Press, vol. 17(02), pages 283-295, April.
- Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:159:y:2010:i:1:p:151-165. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
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.